Bruno Fernandes opened the scoring a minute into the clash after Gabriel Jesus fouled Anthony Martial in the box, the Portuguese midfielder made no mistake from the spot.
Luke Shaw added the second goal just after the restart to end Manchester City‘s winning run.
Solskjaer has expressed his delight after ending their rivals winning run.
“I’m delighted. We were on the front foot for 10-15 minutes but then the last half hour of the first half we played too much on the result. We had to get to half-time to get hold of everyone again.
“We defended really well. We were more like ourselves with the ball attacking-wise.
“Anthony Martial was man of the match and he was an even bigger doubt than Luke. That was the Anthony we know – strong, positive and taking players on. I’m delighted for him.”
Manchester City are back in Premier League action on Wednesday.