It was the Foxes' seventh win in a row and took them eight points clear at the top of the Sky Bet Championship table.
After a forgettable first half when both sides struggled in difficult conditions following a torrential thunderstorm, the Foxes took control after half-time.
Middlesbrough were undone by the pace of Vardy up front and he put Leicester ahead with his 10th goal of the season in the 52nd minute. But Boro protested furiously, complaining that the ball had gone out of play in the build up to the goal.
Vardy was in the thick of things again in the 71st minute, racing into the penalty area before being brought down by Rhys Williams. But Shay Given saved Nugent's spot kick - his 12th penalty of the season nine of which have been successful.
Two minutes later however, Williams flattened Vardy again, and from Matty James' free kick, Ritchie De Laet scored with a far post header.
The win extended Leicester's unbeaten record against Middlesbrough to 13 matches.
Pearson said: "It was a very good win in difficult conditions in the first half. That probably suited them more than us because we were not able to play the type of football we have been accustomed to at home.
"But we stuck at it, limited their opportunities to a minimum and, as the weather improved, so did our effectiveness on the game.
"This season more than ever, we have developed a way of playing that has brought us good results. And I thought the players coped with the conditions pretty well and in the second half it was a decent game of football.
"Vardy did what he has been doing all season - occupying a back four, working hard and converting chances. It is a big plus for the side. His contribution has always been valued by his peers and this season his conversion rate has been better. His contribution was very good.
"We have now got 60 points from 27 games which is good going. The challenge now is to see it through and the players are determined to do so."
Middlesbrough head coach Aitor Karanka said that they had been beaten by "the best side in the league" but felt Leicester's first goal should have been disallowed.
Karanka said: "Before the game I said Leicester were the best team in the league. I still say that now but they did not need any extra help from the referee.
"But we need to learn that if you concede the first goal or make a mistake you have to keep working in the same way throughout the game.
"We did well in the first half and had chances to score but in the second half they were more intelligent than us. They took advantage of the referee's decision and raised their game while we went down.
"We could have been better in the second half. The game is not over because you concede the first goal. We felt the ball had gone out of play in the build up to the first goal but that is no excuse."