The Belgian started his masterclass with a wonderful first-time finish into the roof of the net from Gabriel Jesus' cutback in the second minute.
Man City doubled their advantage 13 minutes later, with De Bruyne squaring for Raheem Sterling to tap into an empty net.
De Bruyne scored his second five minutes before half-time, curling a low shot into the bottom-left corner from just outside the penalty area.
Then he was denied a first Premier League hat-trick by a terrific Bernd Leno save from his long-range shot.
Third-placed Man City are now on 35 points, four behind Leicester City in second. Arsenal sit ninth with 22 points.
Arsenal: 21 Dec v Everton (A)
Man City: 21 Dec v Leicester (H)