Dieng made two free throws with 12.7 seconds left for a four-point lead, and after the Panthers' Lamar Patterson shot an air ball with 6 seconds left, Smith followed with two more free throws for a 64-58 lead with 4.2 seconds left.
Woodall, who had 14 points, drained a long three-pointer in the final second.
Smith finished with 20 points while Dieng had 14 points, 12 rebounds and five blocks for the Cardinals (17-4, 5-3 Big East).
"I think this win will help us a lot, move our confidence up a little bit too," Dieng said.
In another Top 25 game *
At West Virginia, No. 3 Kansas (19-1, 7-0 Big 12) got a scare but extended the nation's longest winning streak to 18 games with a 61-56 victory over the Mountaineers (9-11, 2-5).
Syracuse freshman forward Dajuan Coleman will have a surgical procedure on his left knee Tuesday. Coleman, who has started all 20 of the sixth-ranked Orange's games this season, is expected to miss 4 weeks. He was injured in practice before the Villanova game on Saturday.