But Leicester took the chance to equalise after Rob Hulse upended Joey Gudjonsson, who then picked himself up to score the resultant penalty.
Kilgallon restored Leeds' advantage from 12 yards before Patrick McCarthy was dismissed for foul language.
Leicester boss Craig Levein on Kilgallon's winning goal:
"It was struck from outside the area and hit a player stood right in the middle of the six-yard box.
"I don't understand how anyone can say he wasn't interfering with play. The linesman has made a big mistake.
"I am not condoning what Paddy McCarthy did - it was wrong to go running to the linesman - but the goal changed the game and it took us down to 10 men."
Leeds: Sullivan, Kelly, Butler, Kilgallon, Harding, Miller, Walton (Richardson 84), Lewis, Hulse, Blake (Pugh 90), Healy (Moore 90).
Subs Not Used: Bennett, Crainey.
Booked: Kelly.
Goals: Healy 41, Kilgallon 73.
Leicester: Douglas, Stearman, Gerrbrand, McCarthy, Maybury, Sylla, Gudjonsson, Kisnorbo (de Vries 81), Smith, Hume, Hammond (Dublin 87).
Subs Not Used: Tiatto, Johansson, Hamill.
Sent Off: McCarthy (75).
Booked: Smith.
Goals: Gudjonsson 69 pen.
Att: 21,402
Ref: M Dean (Wirral).