The Cardinals held just a 63-61 lead before Garcia sank a pair of free throws with a minute remaining. After Louisiana-Lafayette's Dwayne Mitchell was whistled for traveling, Louisville's Ellis Myles was fouled but missed two from the line with 41 seconds to play.
After Mitchell split a pair of free throws nine seconds later, the Ragin' Cajuns let the clock tick down until 14 seconds were left before fouling Garcia - an 87 percent shooter from the line. The junior forward calmly sank a pair of free throws for a 67-62 cushion.
Mitchell missed two free throws before Louisville's Taquan Dean split a pair with 3.1 seconds left to cap the scoring.
Brian Hamilton collected 19 points and 10 rebounds before fouling out in the waning seconds for the Ragin' Cajuns (20-11), who won the Sun Belt Conference tournament in Robert Lee's first season as coach.