Kelechi Iheanacho’s 17th goal of the season – his 14th in his last 14 games – earned a battling 2-1 win after the Eagles gave the hosts a scare.
Wilfried Zaha put Palace in front before Timothy Castagne and Iheanacho struck to move Leicester seven points clear of fifth-placed West Ham in the Premier League.
Three wins from their final five games would guarantee the Foxes, who are third, a top-four spot.
“We had that hunger and desire. It’s a real collective win,” said Rodgers.
“I always look forward and never behind, there are still five games to go and tonight we equalled our points total from last season (62). Now we can recover from three tough games in nine days.
“We are constantly looking to improve. Each year you are always looking to improve in terms of maturity and football.
“We have matched last season and if we can gain more points in the next five games it shows we are developing. I get great joy seeing these guys getting better every day.
“It was a different type of game, we went behind and playing against one of Roy’s teams it was going to be a real test for us.
What was really pleasing was the patience we kept
“We said at half-time about keeping calm and the goal early in the half was wonderful and that set the tone for us.
“What was really pleasing was the patience we kept. With a bit more finesse we might have had a couple more goals.”
Palace scored with their first attack after 12 minutes when Ebere Eze fed Zaha and he beat Kasper Schmeichel for his 10th goal of the season.
Initially Leicester struggled to recover during a disjointed first half but levelled five minutes after the break when Castagne collected Iheanacho’s pass and drilled in from 10 yards.
Jonny Evans kept them level soon after with a wonderful last-gasp tackle to deny Christian Benteke a tap-in after Jairo Riedewald had broken clear but the Foxes kept pressing.
James Maddison and Jamie Vardy shot at Vicente Guaita before Vardy had a goal disallowed for offside.
It was in danger of becoming a frustrating night for the hosts before Iheanacho collected Evans’ long ball, cut inside Scott Dann and blasted past a static Guaita from an angle with 10 minutes left.
“At half-time I thought we might go on to win,” said Palace boss Roy Hodgson, with the Eagles 13th.
“It was a bit of a disappointment to leave here with nothing.
“If we hadn’t conceded the goal so early in the second half, our confidence would have been high. The equaliser came too early after half-time.
“We didn’t get enough time to enjoy the fact we were leading. I honestly thought we’d see the game through but I was wrong.
“We fell foul to a wonderful Iheanacho strike 10 minutes from the end.”