Louisville remained unbeaten by overcoming a nine-point Vanderbilt lead in the second half and a five-point advantage by the Commodores in the extra period.
Siva's game-winning shot saved teammate Chane Behanan from the embarrassment of costing his team a victory. Behanan missed a wide open layup just before the buzzer at the end of the second half that would have wrapped up a Louisville win.
Instead, the Cardinals (7-0) had to come from behind in the overtime and they took a 58-57 lead with 1:02 remaining on Kyle Kuric's 3-pointer. Brad Tinsley tied it by making 1-of-2 foul shots, but Louisville went back in front on a Kuric jumper with 33 seconds left.
Two free throws by John Jenkins with 12 seconds to go again tied the game, setting up Siva's drive through the Vanderbilt defense for the winning basket.
Kuric led the Cardinals with 15 points and Siva had 14. Vanderbilt (5-3) was paced by Jenkins with 27.
Louisville is one of 18 unbeaten teams remaining in major college basketball. Auburn dropped out of the unbeaten ranks Friday by losing to Seton Hall, but Syracuse, Northwestern and Missouri all kept their streaks going.