An own goal from Leart Paqarada on the hour set Ukraine on the way in the Group I match before Andriy Yarmolenko sealed their win to put them level on 17 points with second-placed Croatia, who were surprisingly held 1-1 at home by Finland.
With leaders Iceland (19 points) hosting Kosovo on Monday and set to top the group, Ukraine's meeting with Croatia in Kiev is likely to decide who earns second place and a possible spot in the European playoff round.
The match was played in the Albanian city of Shkoder as Kosovo do not yet have any stadiums considered fit for World Cup qualifiers.
It was a laboured performance from Ukraine although it might have been easier if Yevhen Konoplyanka's first-half solo effort had gone in rather than striking the woodwork.
A disciplined Kosovo did well to frustrate the visitors until Konoplyanka crossed to the far post and the hapless Paqarada turned the ball into his own net.
Yarmolenko wrapped things up with en emphatic finish three minutes from the end.
The winners of the nine European groups qualify directly for Russia next year and the best eight runners-up play off for four more places.
(Writing by Brian Homewood in Berne; Editing by Toby Davis)
