Aaron Horton's goal with less than a minute to play propelled Louisville to victory as UofL fans rushed the field in celebration.
UCLA jumped to a 2-0 lead in the first 17 minutes of action on a goal by Eder Arreola and Kelyn Rowe.
Louisville's Colin Rolfe cut the margin to 2-1, but UCLA's Chandler Hoffman scored a few moments later to give the Bruins a 3-1 advantage.
Charlie Campbell's goal for Louisville cut UCLA's lead to 3-2 at the 39 minute mark. Louisville tied the game at 3-3 in the 47th minute on Rolfe's second goal of the contest.
Nick DeLeon gave Louisville it's first lead 4-3 in the 56th minute, but UCLA tied the game on Victor Chavez goal in minute 80.
That setup up Horton's game-winner to cap UofL's miraculous comeback and keep the Cardinals dream season alive.
Next up for Louisville is a national semifinal matchup against UNC Dec. 10. The winner of that contest will play for the NCAA Tournament title on Dec. 12.