Sunday's 3-0 loss to Ukraine in a Group I game staged in Poland meant the Kosovans have conceded nine goals this week at neutral venues.
Fresh off a 6-0 "home" loss to Croatia which was actually played in Albania because Kosovo still doesn't have a certified stadium, Kosovo had to face Ukraine in Poland because the Ukrainian government doesn't recognize the tiny Balkan nation's independence.
Second-best for most of the game, Kosovo nevertheless kept the margin to 1-0 until the 81st minute, when Andriy Yarmolenko scored one goal, then set up another, to end a five-game winless run for Ukraine.
Ukraine took the lead thanks to Artem Kravets' deflected first-half goal. Kosovo could have taken something from the game, with Ukraine goalkeeper Andriy Pyatov coming close to an own-goal in the 61st before a Kosovan shot rattled the crossbar minutes later.
Ukraine was angered by having three close penalty appeals turned down, but nerves were calmed when Yarmolenko controlled a cross from substitute Alexander Karavayev and slotted it into the net. Soon after, he set up the third goal for Ruslan Rotan, who had seen an earlier strike ruled out because offside players were interfering with play.
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