Milwaukee superstar Giannis Antetokounmpo was held to 12 points but grabbed 23 rebounds before fouling out in the second overtime.
The Raptors led by as many as 11 points but had only a two-point advantage entering the fourth quarter.
They then reclaimed an eight-point lead when Leonard made a three-pointer with nine minutes and five seconds to play, but the Bucks managed to claw themselves back to 96-96 by full-time.
In overtime, Toronto again squandered a four-point advantage to send the match to second overtime, before Leonard finally put the match to bed.
Leonard made 11 of 25 shots and went 12 for 13 at the free throw line.
He had nine rebounds and five assists despite appearing to be bothered by leg pain.
«I’m feeling all right. This is play-off basketball … everybody’s hurting so I’ve just got to keep fighting,» Leonard said.
The winner of the eastern conference finals will likely face Golden State in the NBA finals, with the Warriors up 3-0 in their series with Portland.