Tony Pulis' men grabbed the 1-1 draw, which made their final match away to Besiktas an irrelevance from their point of view, after Matthew Upson's 27th-minute own goal had given Kyiv the lead.
Ricardo Quaresma struck a dramatic injury-time winner for Besiktas, whose 3-2 win over Maccabi Tel Aviv in Israel means they will join Stoke in the next stage if they earn at least a point from their final match.
Quaresma and Ibrahim Toreman had put the Turkish side 2-0 up either side of half-time, but Shiran Yeini and Moshe Lugasi looked to have grabbed a vital point for Maccabi until Quaresma struck with his second.
Romanians Vaslui fought a fine rearguard action to claim a goalless draw at home to Serie A giants Lazio and leave themselves a fine chance of progressing as runners-up from Group D.
PSG in trouble
Sporting wrapped up their place as group winners after a 2-0 win over FC Zurich, goals from Ricky van Wolfswinkel and Valeri Bojinov seeing the Portuguese side home in comfortable fashion.
Vaslui's point leaves them locked together with Lazio heading into the final set of games, with the Romanians away to rock-bottom Zurich and Lazio at home to the group winners.
Athletic Bilbao's 2-1 win over Slovan Bratislava earned their qualification from Group F as pool winners, thanks to goals from Oscar de Marcos and Markel Susaeta.
Paris Saint-Germain's surprise 2-0 defeat to Salzburg gave the Austrians an advantage as they now sit in second place. The French side will now have to better Salzburg's result on the final matchday to qualify.