City made heavy weather of beating the brave Faroe Islanders, and it was not until early in the second-half that Martin Petrov struck to ease any worries amongst the Manchester fans who had travelled to Yorkshire for this second-leg.
But the result on the night was completed when Darius Vassell raced into the area before rounding Torgard and slotting the ball home.
City manager Mark Hughes said: "They defended extremely well. It was damage limitation from them really, but you have to give them praise for their efforts.
"Their goalkeeper had a wonderful night, they threw bodies in the way of everything and made life very difficult for us.
"I was pleased with my lads. They kept at them and if their goalkeeper had not had such a great night, we would have won it at a canter.
"But frankly we were never in any danger. We should have won by a fair margin and we should have been quicker in possession but the key is that we have qualified for the next round, that was the objective."