Stoke 1-1 Dynamo Kiev: Jones scored, Upson own-goal
Kenwyne Jones headed home the equaliser as Stoke drew 1-1 with Dynamo Kiev at the Britannia Stadium to reach the Europa League last 32.
Tony Pulis's side were outplayed in the first half and went in a goal down at the break after Matthew Upson had prodded Oleksandr Aliyev's shot beyond his goalkeeper Asmir Begovic on 28 minutes.
The Premier League team looked set to need the daunting prospect of a draw against Besiktas in Istanbul in their final match on December 14 until Jones popped up to nod Jermaine Pennant's cross into the unguarded net to hand Stoke the point they craved.
Besiktas - 3-2 winners over Maccabi Tel Aviv in Israel - will go through as Group E winners if they down Stoke in the group's concluding match, but at least the visitors do not need a result from that trip.
Kiev conclude their campaign with a home match against Maccabi on the same night, but require a Stoke win in Turkey to keep alive their hopes of progress.
The Ukrainian side thought they had snatched a dramatic win in injury time, but the much-maligned Begovic performed heroics when he dived at full stretch to tip Andriy Yarmolenko's long-range effort past a post with a breathtaking save.
Kiev probably paid the price for failing to press home their advantage when they outplayed and outpassed the home team for most of the first hour.
The warning signs were already there before Kiev struck as Begovic saved from Aliyev on five minutes before Aliyev hammered an effort wide of goal on 10 minutes.
Andriy Shevchenko then thumped a shot into the side of a post on 36 minutes with the home fans still reeling from seeing their side - unbeaten in Europe this term - fall a goal behind.
Stoke emerged after half-time looking a bit more like themselves as they were finally rewarded for increasing the tempo against a visiting side suddenly content to sit on their one-goal lead.
Wilson Palacios forced Dynamo keeper Olexander Shovkovskiy to make his first real save of the night on 51 minutes before Pennant saw a blistering effort beat Shovkovskiy only to be hacked off the line by Yevhen Khacheridi.
But Pennant was to be the catalyst for the Stoke revival as he unearthed a sublime cross from out wide that fell perfectly on Jones's head for the goal that delighted the home supporters.
Amid the feeling of euphoria and relief at the full-time whistle, there was also the welcome sight of substitute Ricardo Fuller appearing for the first time since he ruptured an Achilles tendon in April.
Stoke City: Begovic, Shotton, Huth, Upson, Higginbotham, Pennant, Palacios, Diao, Delap, Jones, Jerome; Subs: Nash, Fuller, Wilson, Shawcross, Whitehead, Walters, Crouch
Dynamo Kiev: Shovkovskiy, Danilo Silva, Yussuf, Khacheridi, Betao, Gusev, Aliev, Vukojevic, Yarmolenko, Ideye, Shevchenko; Subs: Koval, Milevskiy, Haruna, Adi, Ninkovic, Leandro Almeida, Correa