Leonard scored 36 points, including eight in the second overtime, and Toronto beat Milwaukee 118-112 to cut the Bucks' lead in the NBA Eastern Conference finals to 2-1.
Leonard also had nine rebounds and five assists in more than 52 minutes of action despite some leg discomfort.
Siakam had 25 points and 11 rebounds but he missed a pair of free throws with 7.4 seconds left in regulation that could have iced the game.
The Raptors will try to level the best-of-seven series when they host Game Four tomorrow (HK time).
Giannis Antetokounmpo had 12 points and 23 rebounds for the Bucks before fouling out late in the second overtime.
Toronto's Kyle Lowry and Norman Powell fouled out in the fourth quarter.