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.
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.