After an opening win against Monaco two weeks ago, Griezmann's double – and Koke's late strike – has given Diego Simeone's side a perfect platform to progress from Group A.
The World Cup winner put his side ahead with a typically assured strike before Arnaut Groeneveld gave the Belgian champions an unlikely leveller with a stunning effort.
Griezmann then proved exactly why he is Atletico's talisman in the 67th minute, producing another clinical finish to set Los Rojiblancos on their way to three more points, which were sealed by Koke.
Atletico rarely threatened during a tepid opening, with Saul Niguez's wayward volley from close range their one clear sight of goal in the first 25 minutes.
Only a superb last-ditch tackle from Stefano Denswil prevented Thomas Lemar from finishing a flowing move before Griezmann broke the deadlock in the 28th minute, sliding coolly past Karlo Letica from eight yards after Lemar's cross had found him at the back post.
The visitors bounced back in style six minutes before the interval, though, Groeneveld unleashing a fierce effort from 25 yards that fizzed past Jan Oblak to pull them level.
Saul flashed a header narrowly over shortly after the restart, while Letica smothered Griezmann's effort just after the hour mark.
The Frenchman did net his second of the night soon after, stroking into Letica's bottom-left corner from Diego Costa's selfless pull-back.
Substitute Angel Correa blazed over with just Letica to beat late on and Atletico grabbed a third deep into stoppage time when Koke clipped home after Griezmann's surging run down the left.
What it means: Atletico and Dortmund setting the pace
Borussia Dortmund's win over Monaco in the group’s other game means that Simeone's side and the Germans have maximum points after two games. With back-to-back matches between the two coming up, we could soon have a clearer picture of who will finish as group winners. Brugge, meanwhile, sit rock bottom alongside Leonardo Jardim's beleaguered French outfit and might already have one eye on a third-placed finish and a run in the Europa League.
Griezmann sparkles again
It is little wonder Aletico were so eager for Griezmann to resist the overtures of Barcelona during the off-season. The Frenchman again showed off his full repertoire against Brugge, scoring twice and setting up Koke's late third with some dazzling wing play.
Costa's torrid season continues
The Spain striker has been a shadow of his former self since returning to the Wanda Metropolitano and his woes in front of goal continued against Brugge. With just one goal so far this campaign, it is hardly surprising that the former Chelsea forward looked desperately short of confidence in what was a limp display.
Key Opta facts
- Atletico Madrid have now won six consecutive home matches in all European competitions, their best such run since November 2012 (12 games).
- Club Brugge have lost eight consecutive Champions League games; only RSC Anderlecht (12 in November 2005) have had a longer such run among Belgian clubs in the competition.
- Atletico have conceded as many goals in their last five home Champions League games (five) as they had in their previous 22 combined.
- The team playing at home has now won all five meetings between Atletico and Brugge in all European competitions (three for Atletico, two Brugge).
- Antoine Griezmann has been directly involved in 17 of Atletico's last 20 Champions League goals scored at home (13 goals, 4 assists).
Simeone's side return to LaLiga action on Sunday when Real Betis visit the Spanish capital, while Brugge travel to Standard Liege on the same day in the Belgian First Division A.