Lloyd Dyer claimed Leicester's other goal in a one-sided contest at the King Power Stadium.
Burnley lost 2-1 at Huddersfield, Oliver Norwood and James Vaughan from the penalty spot with the crucial home goals.
Danny Ings' reply came too late for the visitors, who also ended the match with 10 men following the last-minute dismissal of Michael Duff.
QPR slipped up 2-1 at Doncaster, Harry Redknapp's side undone by strikes from forward Theo Robinson and defender Paul Quinn.
Charlie Austin had given Rangers the lead but they were unable to hold on and Quinn's effort a minute from time snatched the points for Rovers.
Blackpool's 2-0 victory over Sheffield Wednesday keeps them fourth in the table, courtesy of goals in each half from Ricardo Fuller and Dan Gosling, while Wednesday suffered their seventh defeat of the season and sit second from bottom.
Yeovil climbed off the table's foot with a 3-0 home win over Watford thanks to goals from Byron Webster, Ishmael Miller and Joe Edwards.
Blues right-back Paul Caddis scored his first-ever goal for Birmingham, then followed it up with his second before Nikola Zigic completed the comprehensive win.
Tommy Smith headed the winner for Ipswich in a 1-0 success at Charlton, while Middlesbrough saw off Bolton by the same scoreline thanks to Grant Leadbitter's penalty.