Second-half goals from skipper Wes Morgan and substitute Andy King, gave the Foxes the win after a spirited performance from Peterborough in the first-half.
Kasper Schmeichel palmed away a fierce shot from Paul Taylor at the start of the second half, but, as the visitors ran out of the steam, the Foxes took charge and a towering header from Morgan in the 50th minute followed by a superb strike from substitute Andy King 25 minutes later, gave them a comfortable victory.
A delighted Pearson said: "It was a good result, and it was a tougher game than people probably expected. Peterborough pass the ball exeptionally well and I'm sure their game plan was to keep it tight, keep possession and get us frustrated.
"But I was very pleased with how we coped with that. Even in the first half when we didn't have as much of the ball as I would have liked, we still created the best opportunities.
"We pressed higher up the pitch in the second-half and won the ball back in dangerous areas. So, all in all, it was a good day's work and a professional performance.
"It is good to get off to a winning start because we know the expectation on us is going to be there. We all want success here - the owners, players and the fans.
"We all want to do it, but it is going to be hard work for us.It is a very difficult division to get promoted.
"We have a tough opening 10 games so we need to do well at home and it was good to start with a win."
Peterborough manager Darren Ferguson believes the Foxes have a good chance of promotion.
He said: "The key appointment for them was giving Nigel the job. He knows the club.
"It was a tough opening game for us but there was a lot of positives to come out of it.
"We dominated the first half but did not create enough chances. The key moment was their first goal. It was a blatant foul. Their centre-half has got both hands on my centre-half.
"That was disappointing.The goal gave them impetus and they got on top. It was just a pity we could not get our noses in front before half-time. So a lot of positives, but a poor result from our point of view."