Second half goals from Dean Whitehead and Peter Crouch sealed the three points for The Potters, with Roberto Colautti getting a last minute consolation for the hosts.
The win ensures the Britannia Stadium outfit keep their place on top of Group E, and look odds on to guarantee qualification to the knockout stages.
Given the long trip Tony Pulis’ men had to endure to play the game, the Welsh manager was happy with the side’s performance.
“I thought the lads were brilliant tonight,” Pulis told Sky Sports.
“The balance looked good. The three centre-halves were very solid. There was a bit of a lapse at the end but that’s a little bit of tiredness I think.
“I’m very pleased. They huffed and puffed a little bit but I thought we coped with it smashing,” he stated.
Stoke host Kiev in their next group game, and Pulis knows that a win will mean topping the group.
“Kiev at the Britannia now is a cup final.
“If we win the game, we’ll win the group, and if we don’t get beaten, we’ll go through, it’s as simple as that.
“It’s a massive game for us and I’m sure it’ll be a great night because they are a good side. I think it’s the toughest group so, if we do it, it’s a big achievement, but we still have to do it,” he concluded.
Domestically Stoke face a trip to Bolton on Sunday, and will look for three points to bring them back into the top half of the table.
By Gareth McKnight