The Ukrainians have 18 points ahead of their final match against bottom team San Marino, who are without a point from nine games, on Tuesday.
Winger Yarmolenko was unmarked in the middle of the area in the 64th minute at the Metalist Arena and collected a perfect cross from Evhen Konoplyanka before curling the ball into the top corner of the net.
The home team looked timid in the opening half while Poland, who needed a victory to keep their qualifying hopes alive, twice went close to scoring.
Konoplyanka cleared the ball off the goal-line following a header from striker Robert Lewandowski and Waldemar Sobota forced a good save from keeper Andriy Pyatov with a powerful angled shot.
Yarmolenko then put Ukraine in front before unmarked Borussia Dortmund forward Lewandowski missed an excellent chance to equalise 10 minutes from time when he headed the ball over the bar from close range.
(Writing by Igor Nitsak; editing by Tony Jimenez)
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