JayVaughn Pinkston, Villanova's 6-foot-7, 240-pound junior, scored a team-high 26 points while adding five rebounds, three assists and no turnovers.
"JayVaughn was a beast inside," Wright said.
Guard Davon Usher had 27 points for Delaware (2-3).
The Blue Hens, who look like they will be a serious threat in the Colonial Athletic Association, tied the score at 76 on a deep three-pointer by Usher with 3 minutes, 2 seconds left.
Villanova then scored seven unanswered points. Pinkston earned a conventional three-point play after scoring on a power move and hitting the free throw with 2:48 left.
Ryan Arcidiacono hit two free throws with 1:17 remaining. Following a Delaware turnover, Pinkston hit two free throws to boost the lead to 83-76 with 37.3 seconds remaining.
That was enough to finally hold off the pesky Blue Hens.
While Pinkston was an inside force, he prides himself on his versatility.
"Whatever we need I think I can do," he said. "If coach needs me to play defense, that is what I do and if he needs me to score, that is what I can do."
This was the first down-to-the wire game for Villanova and guard Darrun Hilliard, who had 15 points, 9 rebounds, 6 assists and 2 steals, felt the Wildcats needed a nail-biter.
"It kind of woke us up," Hilliard said. "The last few games were pretty good wins and we were kind of due for a gut check."
Despite taking Villanova to the limit, the Hens said that their confidence didn't grow from this outing.
"I believe each guy on our team doesn't shy away from anybody," said Delaware point guard Jarvis Threatt, who had 16 points and eight assists, but shot just 7 for 24 for the field. "The confidence was already there."
Notes: Villanova sophomore guard Dylan Ennis got the cast off his broken right hand Friday and has been cleared for basketball activities. . . . Delaware played without guard Devon Saddler. He was suspended on Nov. 12 for a month for violating university and team policies.