Louisville Coach Rick Pitino insisted that Louisville (17-6, 7-6 C-USA) was not struggling after an overtime defeat at Cincinnati on Saturday.
But his Cardinals turned in another sub-par performance that resulted in their sixth loss in seven games.
Greer's jumper with 3:09 remaining gave DePaul (16-8, 9-4) the lead for good at 59-58. Drake Diener split a pair at the line with 11 seconds to go for the final margin.
Louisville had a last chance to win the game, but Larry O'Bannon lost control of the ball in the final seconds.
The Cardinals fell into a sixth-place tie with St. Louis in the conference.
The Blue Demons, who have won six of seven, ended a nine-game road skid against the Cardinals.