De Bruyne opened the scoring in the fifth minute, blasting into the top corner to mark his 200th league appearance for City with a goal.
Gundogan doubled the lead shortly after, making him the top-flight’s leading German goalscorer, but he reserved a special mention for his teammate after the game.
“We all know he’s our key player,” he said. “If he’s on form, we’re always able to win the games.
“It’s always tough to come here against a tough and physical side. They have a certain type of playing.
“We needed to be prepared for long balls to their tall striker and it’s about winning second balls and trying to create chances and scoring. Obviously the two goals in the first half helped us a lot.”
The victory at Turf Moor sees City move back to the top of the Premier League table at the expense of Liverpool, with the two teams coming head to head next weekend at the Etihad.
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Gundogan admitted that the City squad understand the importance of not dropping points in the remaining games of the season.
“The next two to three weeks will be decisive but every game feels like a final now to be honest.
“That’s why it was very important to win today. You can’t drop points otherwise it will be punished.”