Roberto de Zerbi says his Brighton side "have a dream" of qualifying for Europe as Solly March's double and a late Danny Welbeck strike condemned Liverpool to a heavy defeat at Amex Stadium.
March converted Kaoru Mitoma's low cross to give the home team a deserved lead, after the returning Alexis Mac Allister had intercepted Joel Matip's loose pass.
The winger then doubled the hosts' advantage with a fabulous left-footed strike from Evan Ferguson's through-ball.
Second-half substitute Welbeck capped a magnificent Brighton display with a superb finish past Alisson after flicking the ball over Joe Gomez.
"I have a fantastic team of fantastic players," said De Zerbi. "It is an honour to work with them.
"We have a target at the end of the season. Now we have to play another 20-21 games and we have to stay focused on those games.
"We want to work harder to achieve our target."
De Zerbi's side dominated the first half but failed to convert their pressure into goals, Trent Alexander-Arnold blocking March's effort near the goal-line and the lively Mitoma poking wide from a tight angle.
Brighton thought they had won a penalty shortly before the break when March went to ground in the area under Alisson's challenge, but referee Darren England overturned his initial decision to award a spot-kick after consulting with VAR.
It mattered little, however, as March netted his third and fourth goals of the campaign before Welbeck struck to lift Brighton up to seventh - one place and two points above their opponents.
Hapless Liverpool well beaten
Defensive frailties and a lack of physicality have proved Liverpool's undoing in recent weeks, with Klopp's side conceding poor goals in defeat at Brentford in the Premier League and a draw at home to Wolves in the FA Cup last weekend.
The visitors, lining up in a 4-3-1-2 formation spearheaded by Cody Gakpo and Mohamed Salah, managed to keep free-flowing Brighton at bay in the first half but created next to nothing themselves and were fortunate to go into half-time on level terms.
Mitoma, in sparkling form for Brighton of late, caused Alexander-Arnold and Matip countless problems, with Salah - or any other Reds player for that matter - failing to offer any protection down their right flank.
Liverpool survived a major let-off when Brighton were awarded a penalty for a foul on March by Alisson, only for VAR to rule that the winger had strayed offside from Adam Lallana's pass.
But the visitors' luck ran out in the second half as March scored twice in the space of seven minutes to put Brighton on course to a fifth win in seven top-flight games.
Gakpo had a close-range effort saved by Robert Sanchez late on, but Welbeck delivered the final blow with a strike that combined skill and audacity in equal measure.
Seagulls going from strength to strength
Mac Allister was handed his first start since helping Argentina to World Cup glory in December, as Brighton made two changes to the team that thrashed Everton in their last league match.
The midfielder paraded his World Cup winners' medal before kick-off and was given a rousing reception by the Seagulls supporters, who were hoping to witness a first home league win over Liverpool since 14 January 1961 - precisely 62 years ago.
Buoyed perhaps by Mac Allister's return to the starting line-up, Brighton played with precision and fluency from the start. March's low shot was brilliantly cleared to safety by Alexander-Arnold, before Mitoma fired past the far post after breaching the Liverpool defence.
While Brighton's opener came from a Liverpool error, there was nothing fortunate about the home side's second as March finished magnificently after being played in by teenager Ferguson, who delivered the latest in a string of eye-catching performances.
Brighton have now scored in each of their last eight games in the top flight, netting 21 goals in that run.
"It's one of the best performances I can remember for a long time," March told BBC Sport. "It's a great day and if we keep playing like that then we'll do well, that's for sure.
"It was just about being patient and waiting for that right pass. We play better against the big teams at home. I don't know why.
"I love playing for Roberto - he's great. He puts his arm around you and tells you you're a good player. Maybe that's what I needed."
Player of the match
WelbeckDanny Welbeck
Line-ups
Brighton
Formation 4-2-3-1
1Sánchez
13Groß5Dunk6Colwill30Estupiñán
25Caicedo10Mac Allister
7March14Lallana22Mitoma
28Ferguson
1Sánchez13Groß5DunkBooked at 17minsSubstituted forWebsterat 90+1'minutes6Colwill30Estupiñán25Caicedo10Mac AllisterSubstituted forSarmientoat 83'minutes7March14LallanaSubstituted forVeltmanat 66'minutes22MitomaSubstituted forLampteyat 90'minutes28FergusonSubstituted forWelbeckat 66'minutesSubstitutes
2Lamptey4Webster18Welbeck19Sarmiento21Undav23Steele27Gilmour29van Hecke34VeltmanLiverpool
Formation 4-3-3
1Alisson
66Alexander-Arnold32Matip5Konaté26Robertson
14Henderson3Fabinho6Thiago Alcántara
11Salah18Gakpo15Oxlade-Chamberlain
1Alisson66Alexander-ArnoldBooked at 65mins32MatipBooked at 18minsSubstituted forGomezat 69'minutes5Konaté26Robertson14HendersonBooked at 30minsSubstituted forElliottat 69'minutes3FabinhoSubstituted forKeïtaat 68'minutes6Thiago Alcántara11Salah18Gakpo15Oxlade-ChamberlainSubstituted forDoakat 69'minutesSubstitutes
2Gomez7Milner8Keïta17Jones19Elliott21Tsimikas28Carvalho50Doak62KelleherReferee:Darren EnglandAttendance:31,645Live Text
Match ends, Brighton and Hove Albion 3, Liverpool 0.
Second Half ends, Brighton and Hove Albion 3, Liverpool 0.
Attempt missed. Adam Webster (Brighton and Hove Albion) header from the left side of the six yard box misses to the right. Assisted by Pascal Groß with a cross following a corner.
Corner, Brighton and Hove Albion. Conceded by Alisson.
Attempt saved. Jeremy Sarmiento (Brighton and Hove Albion) right footed shot from outside the box is saved in the bottom left corner. Assisted by Moisés Caicedo.
Attempt saved. Ibrahima Konaté (Liverpool) header from the centre of the box is saved in the top left corner. Assisted by Andrew Robertson with a cross.
Substitution, Brighton and Hove Albion. Adam Webster replaces Lewis Dunk.
Substitution, Brighton and Hove Albion. Tariq Lamptey replaces Kaoru Mitoma.
Corner, Liverpool. Conceded by Joël Veltman.
Attempt saved. Danny Welbeck (Brighton and Hove Albion) left footed shot from the centre of the box is saved in the bottom right corner. Assisted by Solly March.
Foul by Pascal Groß (Brighton and Hove Albion).
Ben Doak (Liverpool) wins a free kick in the defensive half.
Jeremy Sarmiento (Brighton and Hove Albion) wins a free kick in the attacking half.
Foul by Naby Keïta (Liverpool).
Joël Veltman (Brighton and Hove Albion) wins a free kick on the right wing.
Foul by Naby Keïta (Liverpool).
Foul by Pascal Groß (Brighton and Hove Albion).
Cody Gakpo (Liverpool) wins a free kick in the attacking half.
Substitution, Brighton and Hove Albion. Jeremy Sarmiento replaces Alexis Mac Allister.
Goal! Brighton and Hove Albion 3, Liverpool 0. Danny Welbeck (Brighton and Hove Albion) right footed shot from the centre of the box to the bottom right corner. Assisted by Solly March with a headed pass.
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