Chicharito nodded the equaliser as the teams shared six goals in last year's fixture at Stamford Bridge and followed up his double strike against SC Braga by converting Rafael's driven cross-shot from close range.
It was an excellent finish, even if he may have been fractionally offside when the ball left the Brazilian defender's foot, and took United back above Manchester City to sit only a point behind Chelsea in the table.
"You want to win the big games and Chelsea hadn't lost a match and are top of the league so it was an important win," Sir Alex told MUTV afterwards.
"We could've been four-up as we had some fantastic football through Rafael and Antonio [Valencia] and we tore them apart on that side. I think they took a long time to get their game going but I was worried in the 15-minute period before half time.
"We could've started the game a bit better in the second half but started to play better when they got their second goal. It was a wake-up call to be honest.
"At that point, I had Chicharito warming up and then they had a man sent off so it consolidated that opinion to bring him on. He's brilliant in there. He took a lot of punishment too. There were a lot of tackles against him but he's such a courageous little lad, such a tough, wee cookie, and he's always going to be a threat to defenders. He's scored the winning goal in an important game."