Leonard had four points in the first extra frame. Billy White provided 16 points and 13 rebounds for the Aztecs (34-2), who advanced to the Sweet 16 where they will face Connecticut next week in the West Regional.
Malcolm Thomas (13 points, nine rebounds and four blocks) made a crucial block of a Lavoy Allen shot in the final minute of the second overtime, preserving the win for San Diego State, which squandered a double-digit lead in regulation.
Ramone Moore led the Owls (26-8) with 17 points.
Khalif Wyatt and Juan Fernandez each added 14 points for Temple.