Louisville (27-9) earned a third-round berth against fifth-seeded New Mexico, which was able to get past No. 13 Long Beach State 75-68 later Thursday.
Davidson was sent home with a 25-8 record.
The Cardinals, seeded fourth in the West Region, broke open close game with a 7-1 run that closed the first half. That sent Louisville off with a 33-25 advantage.
Louisville stretched its lead to 45-35 when Siva scored six consecutive points. The Cardinals pushed the score to 59-44 with 3:22 to go. Davidson cut into the deficit with seven straight points but Louisville hit free throws to seal the game.
Siva wound up with 17 points with Chane Behanan contributing 14 and Kyle Kuric 13 and five other Cardinals also scored points.
Davidson got a game-high 24 points from Jake Cohen sand 13 from Clint Mann. However, the Wildcats were just 4-of-19 (21.1 percent) from 3-point range and 21-of-60 (35 percent) from the floor overall.