Nigel Pearson's side have enjoyed a fine campaign in the second tier of English football and their promotion charge showed no signs on stopping at St Andrew's on Tuesday.
Lloyd Dyer opened the scoring on 24 minutes for the visitors and, although Leicester continued to control possession, the scores remained the same until half-time.
It took until the 83rd minute for Leicester to make things comfortable with Jamie Vardy calming the visitors' nerves.
Adam Le Fondre was once more the hero, grabbing his second hat-trick in as many home matches, while Pavel Pogrebnyak and Hal Robson-Kanu also on the scoresheet for Nigel Adkins' side.
Jay Spearing ensured a tense ending in the 85th minute, but Harry Redknapp's men saw out the remaining time.
Doncaster Rovers moved out of the relegation zone with a 3-0 victory over 10-man Charlton Athletic at the Keepmoat Stadium, with Chris Powell's men slipping into the bottom three.
Nick Proschwitz scored on his Barnsley debut in a 2-2 draw with Blackburn Rovers. Tom Cairney and Rudy Gestede had put the visitors ahead before half-time, but Chris O'Grady's penalty secured a point for Danny Wilson's men.
Lowly Millwall came from behind to secure a 1-1 draw with fellow strugglers Sheffield Wednesday. Giles Coke's 69th-minute opener was cancelled out by DJ Campbell's first goal for the club. Coke and Millwall's Shane Lowry were then both shown straight red cards in the closing stages for an altercation in the corner flag.
