Gerrard’s goal came just a day after Liverpool manager Rodgers confirmed the former England captain, whose form has been called into question this term, had been offered a new contract with the Merseysiders.
Simon Mignolet’s own-goal gave bottom of the Premier League Leicester the lead but Adam Lallana quickly levelled before Gerrard put the visitors in front.
Leicester defender Wes Morgan was then sent off at the King Power Stadium before Jordan Henderson sealed a morale-boosting victory for Liverpool late on.
Gerrard had been left out of the starting side in the 1-0 win over Stoke City on Saturday, a match that marked the one-club man’s 16th anniversary as a Reds player, but returned as one of three changes made by Rodgers.
However, Leicester boss Nigel Pearson named an unchanged side despite the Foxes failing to win in their previous eight matches.
Leicester had the game’s first real opportunity when Leonardo Ulloa found strike partner Jamie Vardy but his tame effort was no problem for Liverpool goalkeeper Mignolet.
They should have taken the lead when Mignolet’s poor clearance went straight to Esteban Cambiasso 30 yards out, but the Argentinian side-footed his shot wide with the goal gaping.
– Unfortunate –
Even so, the Midlands club went ahead in the 22nd minute when Riyad Mahrez’s run found Vardy, whose shot was saved by Mignolet.
The ball was kept in play and Ulloa’s shot hit the post, with the rebound going in off the unfortunate Liverpool ‘keeper.
But Liverpool were behind for just four minutes, with Morgan’s defensive header from Lucas Leiva’s cross falling straight to Adam Lallana, who fired past Leicester goalkeeper Kasper Schmeichel from 10 yards.
Leicester continued to attack, though, with Marcin Wasikewski seeing a deflected header go just over from Matty James’s corner.
For the start of the second half, Rodgers brought on Alberto Moreno, who went to left-back in place of Javi Manquilllo with Glen Johnson switching to the right.
Liverpool went on to take a 54th-minute lead with Gerrard starting and finishing the move.
The midfielder fed Raheem Sterling, whose cross was cut out by Morgan only for Gerrard to react quickest to the loose ball to beat Schmeichel with a composed finish.
It was a goal that meant so much to the Liverpool great, with Gerrard sliding on his knees in celebration in front of the away fans before clenching his fist at them.
Gerrard went close to a second when his shot just missed Kasper Schmeichel’s goal, but Leicester were still very much in the game with Wasilewski disappointingly mis-hitting a shot from a Mahrez cross.
But home hopes of a draw suffered a huge setback in the 63rd minute when Morgan brought down England striker Rickie Lambert, who appeared to have got away from him, and was given a straight red card.
Gerrard thought he should have had a penalty following a coming together with Schmeichel after being sent clear by Henderson.
A lively finale saw Mahrez denied by a fine Mignolet save, with Cambiasso’s shot on the rebound hitting Ulloa and going wide.
Leicester continued to make life difficult for Liverpool, with Vardy seeing a shot deflect just wide from James’s corner.
Liverpool, however, put the result beyond doubt seven minutes from time.
Gerrard’s cross was cut out by Wasilewski, but only as far as Sterling whose shot was saved by Schmeichel before Henderson fired into an empty net- AFP