Last season's Championship winners were over-run early on when conceding Robin van Persie and Angel di Maria goals but hit back through a fine Leonardo Ulloa header.
Ander Herrera looked to have put United back in control 12 minutes into the second half, but a David Nugent penalty and Esteban Cambiasso's first goal for the club levelled things up.
Jamie Vardy then edged Leicester ahead with a cool finish and Ulloa capped off a memorable victory when netting from the spot to take his individual tally to five in five games.
Having also prevailed at Stoke City last week, Pearson said: "To gain back-to-back wins in the Premier League is never easy, especially if you are a newly promoted team.
"For us to win away at Stoke and then follow it up by beating one of the major forces in British football is very satisfying. When you add into that coming from 3-1 behind, it is testament not just to our quality, but also the spirit and self-belief."
Man of the match Vardy was a thorn in United's side throughout with his aggressive style of play and gained just reward for his efforts.
The striker told Sky Sports: "It was absolutely brilliant and you can see what it means to the fans. We know we can give anyone a game, we'd looked into them all week and found their weaknesses - we've exploited them today and it showed in the result.
"Obviously we knew it was a tough mountain to climb at 3-1, but we know that we've got goals in us and with the ability in the team we are going to create loads of chances. Today we managed to put them all away."
Cambiasso added: "It is special for me, my team-mates and the supporters. I'm very happy and we can celebrate, but we must quickly move on to the next match."
