Martha Thomas scored twice in the first half for ScotlandScotland all but sealed a place in the Women's World Cup play-offs as a thumping first-half performance was too much for Ukraine in Poland.
Only an unlikely defeat to the Faroe Islands in September would derail Scotland's bid to finish second in Group B behind runaway leaders Spain.
Caroline Weir's early penalty was added to by Erin Cuthbert and a Martha Thomas double, all before half-time.
Scotland could clinch a play-off spot on Tuesday if Ukraine beat Hungary.
Even if they do not, Hungary would need at least a point against Spain, a side they lost 7-0 at home to last September, and hope Scotland do the unthinkable against the Faroes, the group's bottom-side.
Those play-offs could become complicated, with the possibility of having to travel to the other side of the world just to qualify. But pre-match Pedro Martinez Losa's side would have bitten your hand off for the opportunity.
Amidst the emotion of a big night for Ukraine around an hour from their country's border, their players lined up for the anthem draped in the flag of their country in much the same way their men's side had before ending Steve Clarke's World Cup dream.
And they could have been ahead inside three minutes when, after Thomas was denied from close range, Kateryna Korsun galloped up the right wing on the counter attack, picked out Nicole Kozlova in the box, who lashed her shot over the bar.
But the luck was with Scotland. Just four minutes later, Claire Emslie appeared to kick the leg of Korsun but the referee deemed it a foul the other way and pointed at the penalty spot.
Weir duly dispatched the spot kick inside the right-hand post and the Scots were on their way.
Even the lead did not settle Scotland nerves. Lee Gibson's clearance put her defence under pressure, Sophie Howard coughed up possession, and had Anna Petryk managed to hit her shot with more power, Ukraine may well have been level.
Soon, though, it was 2-0. Thomas back-heeled into the path of Cuthbert, who rode a weak challenge and knocked the ball past goalkeeper Kateryna Samson with a composed finish.
Before the game was a quarter of the way through, it was 3-0. Cuthbert's corner found Thomas at the back post who tapped it home.
And in almost a carbon copy of the move came the fourth, again Cuthbert's corner picking out Thomas, who looped a header over a crowded box and into the far corner.
Only a goal-line clearance denied Thomas her maiden Scotland hat-trick before she was substituted along with Cuthbert who failed to shrug off a thumping challenge from Inna Hlushchenko.
Hlushchenko almost made an impact at the right end of the park when her looping shot forced Gibson to tip over the bar in Ukraine's best chance of the game, but Scotland's goal was not to be breached.
Player of the match - Erin Cuthbert
On a night of many impressive performances, Cuthbert's goal and two assists put the game beyond Ukraine.What did we learn?
Scotland so often under Martinez Losa have made it hard for themselves, bossing possession but offering too little in the final third.
And the last time these two sides met, Abi Harrison's 93-minute equaliser salvaged a point.
However, this time it was a hungry and clinical Scotland side who had the game won within 20 minutes.
With Spain out of sight in the group, finishing second was the aim and only a calamity can deny them that now.
What they said
Scotland boss Pedro Martinez Losa tells BBC Sportsound: "I'm sure we can repeat this kind of performance more often. The heart and dedication of the team was very good.
"We knew we could exploit space in behind. We had moments we could control the game in possession. I'm pleased with that.
"In this moment we can't ask the players for more. Ukraine are a good team coached by one of the best in the world. In this moment of the season, every player gave everything.
"It's a step forward. We have to get consistency in the line-up so we can compete. The players are competing for places in training and that's what you want as a manager."
What's next?
Scotland travel to Faroe Islands on 6 September to complete their Group B campaign. Ukraine are in action again on Tuesday when they face Hungary in the same Poland.
Line-ups
Ukraine
Formation 4-3-3
23Samson
18Korsun22Kravets14Shmatko4Romanenko
13Pantsulaia17Apanashchenko3Petryk
16Ovdiychuk19Kravchuk9Kozlova
23Samson18Korsun22Kravets14Shmatko4Romanenko13PantsulaiaBooked at 27minsSubstituted forHirynat 45'minutes17ApanashchenkoSubstituted forKhrystiukat 77'minutes3Petryk16OvdiychukSubstituted forKhimichat 61'minutes19KravchukSubstituted forGlushchenkoat 61'minutes9KozlovaSubstituted forKalininaat 67'minutesSubstitutes
1Boklach2Podolska5Kotiash6Basanska7Kalinina8Kitayeva10Shevchuk11Khrystiuk12Sanina15Hiryn20Glushchenko21KhimichScotland
Formation 4-3-3
1Alexander
11Evans15Howard4Corsie3Docherty
22Cuthbert8Kerr9Weir
19Clelland20Thomas18Emslie
1Alexander11Evans15Howard4CorsieSubstituted forClarkat 85'minutes3Docherty22CuthbertSubstituted forArthurat 74'minutes8Kerr9WeirSubstituted forGrahamat 90+1'minutes19ClellandSubstituted forMurrayat 74'minutes20ThomasBooked at 60minsSubstituted forHarrisonat 75'minutes18EmslieSubstitutes
2Clark5Beattie6Clark7Robertson10Graham12Clachers13Ross14Arthur16Murray17Harrison21Cumings23ArnotLive Text
Match ends, Ukraine Women 0, Scotland 4.
Second Half ends, Ukraine Women 0, Scotland 4.
Foul by Lucy Graham (Scotland).
Anna Petryk (Ukraine Women) wins a free kick in the defensive half.
Substitution, Scotland. Lucy Graham replaces Caroline Weir.
Foul by Chloe Arthur (Scotland).
Tamila Khimich (Ukraine Women) wins a free kick in the attacking half.
Attempt missed. Lyubov Shmatko (Ukraine Women) left footed shot from outside the box is close, but misses to the left.
Substitution, Scotland. Jenna Clark replaces Rachel Corsie.
Corner, Ukraine Women. Conceded by Lee Alexander.
Attempt saved. Inna Glushchenko (Ukraine Women) right footed shot from outside the box is saved in the top centre of the goal. Assisted by Yana Kalinina.
Attempt blocked. Lisa Evans (Scotland) right footed shot from the centre of the box is blocked.
Corner, Ukraine Women. Conceded by Samantha Kerr.
Attempt blocked. Inna Glushchenko (Ukraine Women) right footed shot from the centre of the box is blocked. Assisted by Viktoriya Hiryn.
Attempt blocked. Viktoriya Hiryn (Ukraine Women) left footed shot from the left side of the box is blocked. Assisted by Yuliia Khrystiuk.
Chloe Arthur (Scotland) wins a free kick in the defensive half.
Foul by Yuliia Khrystiuk (Ukraine Women).
Attempt blocked. Tamila Khimich (Ukraine Women) left footed shot from the centre of the box is blocked. Assisted by Viktoriya Hiryn.
Foul by Samantha Kerr (Scotland).
Anna Petryk (Ukraine Women) wins a free kick on the right wing.
