Scotland booked their place in the Women's World Cup play-offs with a thumping first half performance in Poland.
Scotland hopes to finish second in Group B behind Spain if they lose to the Faroe Islands.
Martha Thomas scored twice before the half-time break, as well as an early penalty, which was added to by other people.
If Hungary beats Ukraine, Scotland will qualify for the play-offs.
Hungary would need at least a point against Spain, a side they lost to at home, and hope Scotland do the unthinkable against the Faroes, the group's bottom side.
There is the possibility of having to travel to the other side of the world just to qualify for the play-offs. Pedro Losa's side would have turned down the chance to play.
Their players lined up for the anthem draped in the flag of their country in the same way their men's side did before they were eliminated from the World cup.
They could have been ahead inside three minutes when, after Thomas was denied from close range, Kateryna Korsun galloped up the right wing and picked out Nicole Kozlova, who hit her shot over the bar.
Scotland was the lucky one. Four minutes later, the referee pointed to the penalty spot after a foul was called on Korsun for kicking the ball away.
The Scots were on their way when they got the spot kick.
The lead didn't make Scotland relax. Ukraine may have been level if Anna Petryk had been able to hit her shot with more power.
It was 2-0 soon. Thomas back-heeled into the path of Cuthbert, who rode a weak challenge and knocked the ball into the net.
The game was three quarters of the way through when it started. Thomas tapped the back post to score.
The fourth was almost a carbon copy of the move, with the corner picking out Thomas, who headed into the far corner.
Only a goal-line clearance denied Thomas her maiden Scotland hat-trick before she was replaced by Cuthbert.
Scotland's goal was not to be breached despite the fact that Ukraine's best chance of the game was a looping shot that was tipped over the bar by the Scotland goalkeeper.
Scotland has made it difficult for themselves, offering too little in the final third.
The last time these two teams met, Harrison's 93 minute goal salvaged a point.
Scotland had the game won in 20 minutes.
With Spain out of sight in the group, finishing second was the goal and only a calamity could deny them that now.
Pedro Losa believes that Scotland can repeat the performance more often. The team's heart and dedication was great.
We knew we could take advantage of it. The game was in our hands. I am happy with that.
We cannot ask the players for more. One of the best coaches in the world is in charge of the Ukrainian team. Every player gave their all.
A step forward is what it is. Consistency in the line-up is a must. The players are competing for places in training.
Scotland will go to the Faroe Islands in September to finish their campaign. On Tuesday, Ukraine will play Hungary in the same country.
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