Emmanuel Adebayor raised Arsenal's hopes by making the breakthrough in the 48th minute after getting on the end of Robin van Persie's cross, with a suspicion that the Togo striker handled it.
United, however, rallied through a twice-taken penalty from Cristiano Ronaldo six minutes later and they never looked back. Owen Hargreaves grabbed the winner with a superb free-kick.
Ferguson felt the turning point in the match was the introduction of Anderson and Carlos Tevez 10 minutes into the second half.
He said: "When Arsenal scored it forced my hand, and we were fantastic after that. Wayne (Rooney) could have had a hat-trick.
"But Arsenal had fantastic moments too. It was just an incredible game."
United meet Blackburn next weekend, before travelling to Stamford Bridge to face Chelsea on April 26.
Ferguson added: "If we win the two games now we're champions. We've got over a nervous day today. That was a big, big game - and we've come through it."