After going behind to a Leighton Baines screamer after just four minutes, the Reds struggled to find their rhythm early on.
But the introduction of Ryan Giggs after the break and the decision to move Wayne Rooney from wide left into centre inspired United to a 3-1 victory.
"The change in formation was a big factor," the boss told Sky Sports after the game. "Wayne produced a great performance in the second half after we moved him into the middle.
"Ryan made a real difference when he came on. I was planning to give him about thirty minutes or so but he was keen to get on and I decided to change things at half-time. I thought all the front players were a real handful in the second half and we could have scored a few more goals."
Nemanja Vidic's powerful header drew United level after the break, before Louis Saha fired a sensational second. Ole Gunnar Solskjaer grabbed the Reds' third goal in injury time making it three in two games for the Nowegian.
"Ole's doing very well," enthused Sir Alex. "He's got five goals now and if he carries on like he is doing, and I'm confident will do, he could get us twenty goals this season."
He might not have got on the scoresheet but Wayne Rooney was at the centre of virtually all of United's attacking exploits. Sir Alex was delighted with the England striker's contribution and believes he is well and truly back to his best.
"That was Wayne's best performance of the season so far," declared the United manager. "There were signs before this game that he was coming back to his best and I think the two international games probably helped him with his fitness.
"He had a hand in almost everything we did in the second half, and throughout the ninety minutes I thought he was excellent.
The Reds now turn their attentions to the Champions League ahead of their Group F clash with FC Copenhagen at Old Trafford on Tuesday.
"Cristiano Ronaldo [ankle] should be ready while Darren Fletcher will also be available. We rested Darren for the Wigan game after his exertions for Scotland during the international break, but he'll be okay for Tuesday.
"Gary Neville [calf] could possibly be back but Gabby Heinze is definitely out. We're hoping to have him ready for next Sunday's game against Liverpool."
