Both sides had numerous chances in the first half, but neither were able to take the advantage, heading in goalless at the break.
Paddy Kenny had to work to prevent Anthony Knockaert and Chris Wood from scoring for the home side in the opening 45 minutes, while David Norris and Samuel Byram were both denied by Kasper Schmeichel.
The visitors made a quick start to the second half, Byram breaking the deadlock by blasting the ball in from close range in the 52nd minute.
Ross McCormack almost doubled Leeds' advantage six minutes later, but Schmeichel managed to tip the ball over the crossbar before Knockaert cleared the resulting corner.
Leiecester were awarded a corner deep into stoppage time, with Schmeichel joining his teammates in the penalty area, but it was Keane who got to the ball, nodding it past Kenny to level the scores in the final seconds of the game.
The draw leaves Leicester fifth in the table, while Leeds sit ninth.