Villa seal place in Europa League last 16 as Celtic draw in Italy
Jadon Sancho's header midway through the first half in Istanbul earned Villa a sixth victory in seven European games, clinching a spot in the top eight and allowing Unai Emery's team to bypass the knockout phase play-offs.
Matty Cash struck the post in the second half and Villa held on as goalkeeper Marco Bizot produced a string of key saves with Fenerbahce pushing for an equaliser.
"I'm just happy to get my first goal for Aston Villa and to top it off with that, it's a win," Sancho, who joined on loan from Manchester United in September, told TNT Sports.
"Honestly, I know I can do a lot more. I'm very hard on myself in that aspect.
"It's nice to have a manager that backs you and obviously believes in you. Again, every opportunity I get I'm going to try and do 100% and hopefully I can deliver goals more."
Villa are second in the standings on 18 points and only trail Lyon on goal difference. Lyon won 1-0 at Swiss side Young Boys to ensure their spot in the last 16.
Celtic had to settle for a 2-2 draw away to Bologna, leaving them in danger of failing to advance from the league phase.
Martin O'Neill's side led through Reo Hatate's early strike, but the Japan international was sent off for a second booking on 34 minutes.
American defender Auston Trusty doubled Celtic's advantage before half-time, but Bologna fought their way back with goals from Thijs Dallings and Jonathan Rowe.
Celtic are 23rd in the 36-team table but could be overtaken by a handful of sides playing later on Thursday. The Scottish champions host Utrecht in their final game next week.
"It was a tough ask but the team showed their true mentality. A shame not to get three points, but it's a good point," Trusty told TNT Sports.
"It's something to build on. We've had a strange period, but this team is all about winning. We tied today, but that's the mindset.
"We lost our way a little bit, but now we're finding our way back."
Nottingham Forest are bidding for a fourth win in five in Europe as Sean Dyche's men take on Braga in Portugal.