The Gunners had gone over 500 minutes without netting against the Blues until Alex Oxlade-Chamberlain opened the scoring in the first half, shifting the ball onto his left foot and rifling a thunderous effort into the top corner.
Mourinho tried to rally his side in the second period, bringing on Radamel Falcao, but it was Eden Hazard who had the best chance to level the scores, latching onto Cesc Fabregas' through-ball but blasted over from close range.
Petr Cech, facing his old club, was forced to palm away Oscar's goal-bound free-kick as time ticked away, but Arsenal held on comfortably - and even had two one-on-one chances to extend their lead - to pick up their third trophy of pre-season.
