Unai Emery is looking to win this competition for a fifth time and the favourites to lift the trophy got their campaign up and running in a hard-fought contest.
Villa had only scored twice in their opening six games of the season, both away from home, but they finally grabbed a goal on their own patch courtesy of McGinn's pinpoint strike.
Ollie Watkins came off the bench and saw a penalty saved in the second half as the wait for his first goal of the campaign went on, while 'keeper Marco Bizot made important saves to deliver a much-needed win .
And, following the departure of the club's president of football operations, Monchi, this week, Villa were at least able to give their supporters something to smile about.
Emery made four changes from the side that drew 1-1 at Sunderland on Sunday as he brought in Bizot, Ian Maatsen, Pau Torres and Donyell Malen, while Watkins was one of those to make way.
In Stuttgart, Badredine Bouanani scored his first VfB Stuttgart goal in style to help seal a 2-1 win at home to Celta Vigo.
"I found his finish outstanding, to control the ball like that at that speed was top class," Stuttgart coach Sebastian Hoeness told RTL ahead of travelling to Basel next week. "I think the win was very well deserved ... we were always pushing."
While 20-year-old France-born forward Bouanani made headlines with a deft lob, veteran French striker Olivier Giroud scored a trademark header 10 minutes from time to give Lille a 2-1 victory over Brann.
Twice champions Porto netted late in a 1-0 success at Salzburg while Lyon, who risked missing out on Europe before successfully challenging their Ligue 1 demotion, prevailed 1-0 in Utrecht.
Genk won by the same score at Rangers, ex-Celtic star Oh Hyeon Gyu with the winner after Mohamed Diomande was sent off for the Scots.
Dutch Cup winners Go Ahead Eagles, in the Europa League proper for the first time, had their wings clipped in a 1-0 home defeat by Romania's FCSB.
Viktoria Plze conceded in stoppage time in a 1-1 draw at 10-man Ferencváros, while Panathinaikos won 4-1 at Young Boys having scored three goals in the first 20 minutes.
Norwegians Brann, back in the main draw of European competition for the first time since 2009, were 1-0 down after Hamza Igamane's goal handed hosts Lille a 54th-minute lead.
But Sævar Atli Magnússon bagged a deserved equaliser on the hour - only for Giroud to head home off the bench to become the Europa League's third oldest scorer at 38.
Lille coach Bruno Génésio said: "You could say that a draw would have been a fairer reflection of the game. But we managed to find a way to win with players coming off the bench."
with PA
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