Rodgers was confirmed as Claude Puel's successor just before kick-off at the King Power after dramatically leaving Celtic despite being on course for a third straight domestic treble in Scotland.
The Northern Irishman saw what his new side are capable of as Demarai Gray and Jamie Vardy put the hosts into a 2-0 lead before Davy Propper pulled a goal back.
"I spoke to them about the incoming manager and just said we had to concentrate on the game. He's given the players a boost. He said he's excited to get started," said Leicester's caretaker manager Mike Stowell.
"It's been a difficult season on and off the pitch but I think we should be seventh for the quality we have.
"Today's win broke four defeats on the spin so hopefully the shackles are off because there's still plenty of games to play -- let's look upwards not down."
However, Brighton's alarming slide towards the bottom three continued as they could not find an equaliser and now have not won in seven league games.
Newcastle are headed in the other direction as once again they were inspired by the performance of record signing Miguel Almiron to end Burnley's eight-game unbeaten Premier League run with a 2-0 victory.
Fabian Schar's stunning long-range effort put Rafael Benitez's men in front before Sean Longstaff scored his first league goal for the club to give Newcastle a commanding half-time lead they never looked like surrendering.
"It is amazing to be playing every week, it was my dream as a young boy," said Newcastle native Longstaff.
"There is something different about night games at St James' Park. The atmosphere is the best in the world, I got lost in the goal. It was amazing."
- Everton ready to test Liverpool -
Cardiff remain just a point above the relegation zone as Everton inflicted a second heavy home defeat on the Welsh side in five days with a 3-0 win to boost their confidence ahead of Sunday's Merseyside derby against title-chasing Liverpool.
Gylfi Sigurdsson scored twice either side of half-time before Dominic Calvert-Lewin rounded off a badly needed win for manager Marco Silva in stoppage time.
"The most important thing for us is winning points to boost our confidence and now we have to rest and recover," said Silva, whose side had not played in 17 days.
"We have a big test on Sunday and I know how important it is for the fans and our opponents. We knew how we lost the first game at Anfield and we can achieve victory at our own ground."
Huddersfield remain rock bottom, but did secure their first win under Jan Siewert thanks to Steve Mounie's 91st-minute winner to beat Wolves 1-0.
"I will have one beer tonight –- maybe two. But we have a game on Saturday and there is still something possible," said Siewert, with the Terriers still 11 points off safety.