Bates celebrates his 74th birthday on Sunday and he will fly back to his Monaco base in good spirits after watching Leeds record their fourth consecutive win for the first time since April 2001.
Kilgallon got his boot to Robbie Blake's effort midway through the second half to deflect the ball past stranded City keeper Rab Douglas.
To add insult to injury, Foxes' defender Patrick McCarthy was sent off as Kilgallon celebrated breaking his duck after protesting about the validity of the goal.
It was the perfect response for Leeds after Leicester had levelled the game just five minutes earlier through Joey Gudjonsson's penalty and McCarthy's dismissal left the visitors with too much to do as they desperately chased another equaliser.
Leeds, missing four of their midfield as suspended duo Sean Gregan and Jonathan Douglas joined injured pair Gylfi Einarsson and Shaun Derry on the sidelines, started with a spark and inventiveness that explains their position in the Championship's top four.
They could have taken the lead twice in the opening 20 minutes as their passing cut open the Foxes defence.
Rob Hulse saw his goal disallowed for offside while American winger Eddie Lewis saw him shot smash against the bar after Blake had set him free.
Craig Levein's side were not without enterprise themselves and Leeds - despite their best efforts - were certainly not dominating play.
Ryan Smith forced a fingertip save from Neil Sullivan while Gudjonsson and Elvis Hammond also forced good reactions from the Leeds keeper.
And there was more panic in the Leeds box when McCarthy's header bounced off the bar and hit the back of Sullivan's head before rolling to safety.
But it was David Healy who broke the deadlock, curling home his eighth goal of the season from a well-worked free-kick just before half-time.
Leicester's effort brought them back into the game when Hulse felled Gudjonsson inside the Leeds box, but Kilgallon's winner sent Bates and the rest of Elland Road home smiling.