Chane Behanan added 10 points and nine rebounds for the Cardinals (23-5, 11-4 Big East), who held the Blue Demons to 36 percent shooting and forced 19 turnovers. Smith also had five assists and four steals.
Louisville is unbeaten since it lost 104-101 in five overtimes at Notre Dame on Feb. 9 in the longest regular-season game in Big East history. With the victory over sliding DePaul, the Cardinals moved into a tie with Marquette for second place in the conference behind Georgetown.
Rick Pitino's team visits No. 12 Syracuse, and Notre Dame takes on Marquette in a big slate of games for the Big East on Saturday.
Brandon Young scored 22 points and Cleveland Melvin had 20 for the Blue Demons (11-17, 2-13), who have dropped three in a row and 12 of 13 overall.
Melvin converted a layup to get DePaul within eight with 7:22 remaining, but the Cardinals responded with a 10-0 run to put it away. Siva started the key spurt with two free throws and closed it out with a layup that made it 71-53 with 3:33 remaining.
Young made a 3-pointer with 3 minutes remaining to extend DePaul's streak with at least one 3 to 607 games. But the Blue Demons were just 1 for 9 from long range.
Montrezl Harrell scored 11 points for the Cardinals, and Gorgui Dieng finished with 10.
Louisville and DePaul combined for 23 turnovers, 19 personal fouls and a slew of missed layups during a frenetic first half that included several conferences between the referees and upset coaches trying to angle for calls during the physical play.
Louisville was leading 21-16 when the 6-foot-6 Behanan stole a pass near midcourt, dribbled in and threw down a massive dunk over DePaul guard Worrel Clahar. Behanan was originally whistled for an offensive foul but it was changed to a block on Clahar after a short discussion by the officials, leading to a spirited argument from Blue Demons coach Oliver Purnell.
Behanan then made the free throw to give the Cardinals an eight-point lead with 4:21 remaining. The sophomore forward tacked on another jumper and Luke Hancock hit two foul shots with 43 seconds left in the first half as Louisville carried a 34-25 lead into the break.
The Cardinals shot just 38 percent in the first half, but held the Blue Demons to 27 percent shooting. Neither team had a 3-pointer at the break, combining to miss 10 shots from long range.