The Foxes dominated possession throughout the match and missed chances from Ayoze Perez and James Maddison represented the closest that either team got to scoring in the first half.
Jamie Vardy opened the scoring in the 68th minute to put himself back on top of the top scoring charts, before Maddison's effort into the bottom corner seven minutes later secured the win for the home side.
Leicester move nine points clear of Arsenal in the table as they continue their charge to Europe.
'All round, a really good game for us'
Speaking to Leicestershire Live post match, Rodgers gave an evaluation of his team's performace.
"We were playing against a very good side. I thought we should have been in front in the first half, had a few good chances, but we didn’t become frustrated.
“We came out in the second half, kept our concentration, and I thought once we had the first goal, we had control of the game both with and without the ball, and that’s what really pleased me.
“All round, a really good game for us.”
'He'd press the whole back four if he could'
Speaking further to BBC Sport, Rodgers commended his star striker, stating: "He [Vardy] is up there with the very, very top strikers in European football with what he brings to a team, his pressing. We've allowed him to do essentially what he wants to do - he's so honest, he'd press the whole back four if he could."
He added: "The way it's been going for a period of time now, it's nice because the players know they have the qualities to win any game against any opposition.
"You're playing against a top team with really good players, so you have to be patient but we showed real quality to break through. A very, very important three points."