The victory gave Leicester a four-point lead at the top of the Sky Bet Championship table.
In a remarkable first-half Bolton went a goal down, then twice took the lead only for Leicester to level at 3-3 by the interval. But the Foxes dominated the second-half and, despite a penalty miss by David Nugent, scored two more goals to strengthen their position at the summit.
Danny Drinkwater gave City the perfect start with a rasping 20-yard strike in the fifth minute, only for Bolton to battle back with goals from Andre Moritz and Jermaine Beckford in the 15th and 20th minutes.
Then, in the 41st minute a clearance from Tim Ream struck Matt Mills on the head and flew back into the net for a bizarre own goal that levelled the scores again.
Nugent, after scoring with eight of his previous nine penalties this season, saw Andy Lonergan save his 73rd-minute spot kick but a sensational solo goal by Dyer put the Foxes ahead in the 75th minute and substitute Gary Taylor-Fletcher ensured victory with a neat finish late on.
Pearson said:" I have to admit that the first-half was a bit frustrating in the sense that, to play as well as we did when I thought we were exceptional, to concede three goals was a bit of a shock for us.
"But Bolton were clinical. They didn't create too many chances but the ones they did they really punished us. So you have got to give them a lot of credit for that. For the first 20 minutes we were outstanding and I suppose what it does is it shows you what football is all about. You have got to take advantage when you are on top.
"What pleased me most about the whole game was the fact that our players never lost the belief that they could win. To miss a penalty at 3-3 it could have gone a different way. But we showed a lot of strength today in terms of mental approach but we also showed we have got a good side here.
"I think we showed a lot of quality today. Bolton posed one or two questions for our players but they came up with the answers. And the answers were to keep playing positive football."
Bolton boss Dougie Freedman said: "We set our stall out to score goals. We knew what they were like attack-wise so we felt we had to score goals and we set the team up that way. The plan was working in the first half and I felt it was an end to end game.
"That's the only way you can play against Leicester and we scored three fantastic goals. I was a bit disappointed in the manner of their goals because I think they were a little bit soft.
"But they are a million miles away the best team in this division so to defend against them for 90 minutes is very difficult. That's what happened and, in the end, they got that crucial fourth goal which killed the game off for them and made it very difficult for us to come back.
"But we gave it our best shot against the team who, in my opinion, will be the champions of this division."