Celtic convincingly overcame their nemesis Livingston to restore their three-point lead over Rangers at the top of the Scottish Premiership.
Shortly after Celtic captain Callum McGregor missed a penalty, striker Daizen Maeda headed in the opener from close range after a disputed corner.
A Nicky Devlin own goal and James Forrest's fine finish made it 3-0.
And Andrew Shinnie's close-range reply could not deny Celtic a first win at Tony Macaroni Arena since 2007.
It was a thoroughly professional, clinical and deserved win for Ange Postecoglou's side in his 50th game in charge as they responded to reigning champions Rangers' win over Aberdeen on Saturday.
But Livingston will rue the corner decision that led to Celtic's opener and Ayo Odileye's header against the bar at 1-0 as they passed up a chance to reclaim fourth spot from Hibernian.
With Livingston having taken 17 points since the winter break - a haul bettered only by Celtic - this was very much a game between the Premiership's two form sides.
It looked like Livingston might again spring a surprise as they went close to taking a sixth-minute lead, but Celtic goalkeeper Joe Hart stretched out a big hand to parry clear when Obileye half-volleyed a corner from a difficult angle at the far post.
Celtic responded by dominating possession and took the lead following two minutes of controversy.
When Maeda's attempted cut-back inside the six-yard box struck Jack Fitzwater's trailing arm, the Livingston centre-half appeared to be unfortunate to concede a penalty kick.
Celtic captain Callum McGregor fired the spot-kick against the outside of a post, but the breakthrough was only momentarily prevented.
Anthony Ralston won a corner when the ball appeared to last come off the Celtic right-back's arm and, although Max Sryjek parried superbly from Carl Starfelt's header from Jota's delivery, Maeda was lurking at the back post to provide the vital touch.
It was Celtic's first goal in three meetings with Livingston this season - and it set them on their way to their first win over David Martindale's side.
Although Celtic were now in almost total control, Livingston ought to have gone in at the break level after Alan Forrest's in-swinging free-kick found Obileye unmarked 10 yards out. However, the defender sent his header crashing off the crossbar.
Livingston's dismay was doubled seconds after the break as Ralston's cross into the six-yard box deflected off Obileye's toe, on to fellow defender Devlin's chest, and over the line.
Alan Forrest's form had outshone that of brother James in recent weeks, but the Celtic winger not only kept his younger sibling quiet in their one-to-one exchanges but was the one on the scoresheet on this occasion, racing through to fire low past Stryjek to make it a 13th consecutive season with a top-flight goal.
Shinnie had scored Livingston's winner when Celtic visited in September, but by the time he stabbed home in a crowded goalmouth from a throw-in, the visitors were well on their way to stretching their unbeaten domestic run to 29 games.
Man of the match - Jota
Jota was not so prominent after the break, but the on-loan Benfica winger's clever, incisive runs put Livingston on the back foot from the offWhat did we learn?
Given their record against Celtic - and having only lost once in their previous nine home games - Livingston will no doubt be disappointed to not only have suffered defeat but conceded three goals in the process.
However, Martindale will stress that they still emerge from the weekend well placed to secure a top-six finish and qualify for European football.
The Livingston manager had suggested prior to kick-off that Postecoglou's side are now a different beast from the one that lost in West Lothian in September and so it proved against the only top-flight side he had yet to beat.
Celtic travelled east having only won twice in their last five outings, but two of those were defeats by Bodo/Glimt in the Conference League, and the Australian's side once again showed that they will take some stopping as they look to win the title in his first season in charge.
What they said
Livingston manager David Martindale: "I think Celtic were very good and very clinical. I don't think we deserved much more from the game, but with the two decisions leading to goals you feel a little hard done-by.
"You need a wee bit of the luck to go your way when your playing either of the Old Firm and there's a refereeing decision that leads to the corner - I think it's our bye-kick and the linesman and fourth official told the referee it was a bye-kick.
"On the second goal, I think there's a hand ball from Tom Rogic in the middle of the park and we don't get that decision."
Celtic manager Ange Postecoglou: "Great to win because obviously it's a difficult place to come and get three points. I think our performance was excellent.
"We started the game very well, played at a high tempo and put them under a lot of pressure when they had the ball and created a lot of chances and scored good goals.
"We've got to keep getting stronger and I think we are. We're in a good space to keep getting stronger to the end. We'll be a hard team to stop."
What's next?
Livingston next visit Heart of Midlothian in the Premiership on 19 March (15:00 GMT), while Celtic visit Dundee United in the Scottish Cup quarter-finals on 14 March (19:45).
Player of the match
JotaJota
Livingston
Squad number32Player nameStryjek
Squad number17Player nameForrest
Squad number2Player nameDevlin
Squad number29Player namePenrice
Squad number5Player nameFitzwater
Squad number22Player nameShinnie
Squad number6Player nameObileye
Squad number19Player nameNouble
Squad number33Player nameOmeonga
Squad number8Player namePittman
Squad number18Player nameHolt
Squad number9Player nameAnderson
Squad number24Player nameKelly
Squad number12Player nameSoto
Squad number10Player nameSibbald
Celtic
Squad number17Player nameJota
Squad number38Player nameMaeda
Squad number4Player nameStarfelt
Squad number20Player nameCarter-Vickers
Squad number49Player nameForrest
Squad number56Player nameRalston
Squad number6Player nameBitton
Squad number18Player nameRogic
Squad number3Player nameTaylor
Squad number7Player nameGiakoumakis
Squad number33Player nameO'Riley
Squad number42Player nameMcGregor
Squad number11Player nameAbada
Squad number15Player nameHart
Squad number41Player nameHatate
Line-ups
Livingston
Formation 4-4-1-1
32Stryjek
2Devlin5Fitzwater6Obileye29Penrice
33Omeonga18Holt8Pittman22Shinnie
17Forrest
19Nouble
32Stryjek2Devlin5FitzwaterBooked at 14mins6Obileye29Penrice33OmeongaBooked at 38minsSubstituted forAndersonat 60'minutesBooked at 79mins18Holt8PittmanSubstituted forSibbaldat 76'minutes22ShinnieSubstituted forKellyat 71'minutes17Forrest19NoubleSubstituted forSotoat 70'minutesSubstitutes
3Longridge9Anderson10Sibbald11Montaño12Soto15Boyes16Lewis24Kelly31KonovalovCeltic
Formation 4-3-3
15Hart
56Ralston20Carter-Vickers4Starfelt3Taylor
18Rogic6Bitton42McGregor
49Forrest38Maeda17Neves Filipe
15Hart56Ralston20Carter-Vickers4Starfelt3Taylor18RogicSubstituted forO'Rileyat 75'minutesBooked at 88mins6Bitton42McGregorSubstituted forHatateat 83'minutes49ForrestSubstituted forAbadaat 75'minutes38MaedaSubstituted forGiakoumakisat 75'minutes17Neves FilipeSubstitutes
7Giakoumakis11Abada16McCarthy21Ideguchi29Bain33O'Riley41Hatate57Welsh88JuranovicLive Text
Match ends, Livingston 1, Celtic 3.
Second Half ends, Livingston 1, Celtic 3.
Corner, Livingston. Conceded by Joe Hart.
Attempt saved. Craig Sibbald (Livingston) left footed shot from outside the box is saved in the bottom left corner. Assisted by Sean Kelly.
Foul by Giorgos Giakoumakis (Celtic).
Nicky Devlin (Livingston) wins a free kick in the defensive half.
Attempt blocked. Nir Bitton (Celtic) right footed shot from outside the box is blocked. Assisted by Matt O'Riley.
Giorgos Giakoumakis (Celtic) wins a free kick on the right wing.
Foul by James Penrice (Livingston).
Offside, Livingston. James Penrice tries a through ball, but Ayo Obileye is caught offside.
Matt O'Riley (Celtic) is shown the yellow card for a bad foul.
Foul by Matt O'Riley (Celtic).
Sebastian Soto (Livingston) wins a free kick in the defensive half.
Greg Taylor (Celtic) wins a free kick in the defensive half.
Foul by Sebastian Soto (Livingston).
Hand ball by Greg Taylor (Celtic).
Offside, Livingston. Craig Sibbald tries a through ball, but James Penrice is caught offside.
Attempt missed. Giorgos Giakoumakis (Celtic) header from the centre of the box misses to the left. Assisted by Matt O'Riley with a cross following a corner.
Substitution, Celtic. Reo Hatate replaces Callum McGregor.
Corner, Celtic. Conceded by Sean Kelly.