McGinn opened the scoring in the 11th minute with a first-time finish set up by a driving run from Pau Torres, and was later named Champions League player of the match for the first time in his career at the age of 31.
Emi Buendía and club-record signing Nicolas Jackson also struck as Aston Villa raced into a 3-1 half-time lead at the Jan Breydel Stadium, with Jackson's goal his first for the club since his summer move. Hugo Vetlesen and a Nicolò Tresoldi penalty gave Brugge hope of a comeback, but Unai Emery's side held on for a result that ended a run of three scoreless Premier League matches in some style.
"To get my first Champions League player of the match award aged 31, I'm very happy," McGinn said. "It was so important to show a real gritty performance and get a victory at a very, very tough place to play. The supporters were excellent and Brugge are a very impressive club, so to win tonight was huge for us."
Asked about his goal, the captain explained the thinking behind his finish.
"Pau Torres made a great run through the middle and I just tried to use the defender to elevate the goalkeeper's sight line, so I just passed it in the corner. As I've got older, I've tried to use that finish a lot more and just place it in the corner rather than smashing it."
McGinn praised his side's resilience after the break as Brugge pushed for an equaliser.
"It's a new Villa and it was a big test for the new players to dig in. It was João Gomes and George Hemmings' first Champions League games. It's not easy to go away at a place like this in difficult weather conditions," he said.
"Club Brugge were pushing and pushing and pushing and we had to stand strong. We managed to do that."
The win moves Villa to their first points of the season in any competition and sets up a home league-phase fixture against Fenerbahçe next, part of a run that will also see them face Barcelona, Paris Saint-Germain, Borussia Dortmund, Galatasaray, Viking and Slavia Prague.