Barkley’s deflected strike with five minutes remaining finally decided a chaotic game in which Emery’s team had twice led only to be pegged back.
The victory moved Villa up to third in the group stage table with two matches remaining and has all but guaranteed their place in the knockout stages.
But the target is now to achieve a top-eight finish which would see them avoid the play-off round and progress straight to the last-16.
Emery said: “At the beginning we were trying to be protagonists knowing what we needed to be in the top 24 and now we have the chance to be in the top eight.
“We have two more matches and we will be motivated, our target now is higher than it was when we started this competition.”
John McGinn gave Villa the perfect start at the Red Bull Arena when he fired them in front after just two minutes but a defensive mix-up gifted Lois Openda an equaliser.
Villa went back in front thanks to a superb effort from substitute Jhon Duran, only for Christoph Baumgartner to deliver a brilliant finish of his own after more sloppy Villa defending to level things up again.
Barkley got the winner just two minutes off the bench, his strike hitting fellow substitute Lukas Klostermann and wrong footing goalkeeper Peter Gulasci.
Villa, who have now won three on the bounce in all competitions, next travel to Monaco in the Champions League on January 21 before hosting Celtic in their final group game the following week.
“Today we spoke about the possibility of winning to get in the top eight,” said Emery. “We more or less controlled the game and now we have 13 points and are more or less recovering confidence.
“Hopefully we can keep going and trying to be consistent in the next match against Nottingham Forest. In the Champions League we are feeling strong and comfortable.”