The Foxes looked down and out with 30 minutes remaining when Ander Herrera regained United's hefty cushion, but three goals in the space of 16 minutes turned the game on its head at the King Power Stadium.
It means a second successive top-flight victory for Leicester who are now up to seventh place in the Premier League table.
"Back-to-back wins in the Premier League is never easy, especially for a promoted side," Pearson told BBC Sport. "To back up the Stoke win against one of the big forces in English football is very satisfying. When you add to that coming from 3-1 down, it is a testament to the quality, belief and spirit amongst us.
"All in all we got things right tactically. We were always in the game because we matched them up. The most important thing is we continued in a positive vein. It is not a case of being positive and also being naive. You need to find the right way to approach games. In the end we were full value for it.
"We didn't do it well enough for long periods in the first half but were better in the second. The players have to take credit for how they went about putting into practice what we talked about and also their resilience. It is not just about technical ability."
Next up for Leicester is a trip to face Crystal Palace next weekend.