With the injuries, coach Jay Wright used just seven players, with four of them playing 40 minutes or more.
Villanova led by 39-19 with 1 minute, 53 seconds in the first half and still held a nine-point advantage, 56-47, with 4:26 to play. But the Fighting Irish (19-8, 11-3) embarked on a 13-0 run to take the lead, and almost put the game away in regulation before 'Nova scored the last four points, including Maurice Sutton's follow-up of a miss by Johnson, with 0.9 seconds left to force the extra period.
"Obviously it's a tough loss, a game you wish you never had to experience," Wright said. "We've had a couple of those this year. We're paying our dues. But Notre Dame made some tough shots. We had some good shots, but we missed them."
The Wildcats kept battling in overtime, tying the game at 62 and 65 before Grant gave the Fighting Irish the lead for good with a three-ball with 1:28 remaining. After JayVaughn Pinkston missed a three for Villanova, Connaughton drained his second trey of the period to put the visitors up by six.
Pinkston led the Wildcats with 24 points and Dominic Cheek added 19. Connaughton's 21 points led the Fighting Irish and Jack Cooley added 18 to go with 13 rebounds.
The Wildcats shot just 23.8 percent in the second half and scored only five baskets as Notre Dame put the clamps on them with a zone defense. Each team shot 38 percent in the game.
After going down by nine late in the second half, Eric Atkins scored six points in Notre Dame's 13-0 spurt, including a running bank shot that began a conventional three-point play and gave the Irish the lead, 57-56, with 1:43 remaining. Grant followed with a three-point basket and Notre Dame led by four with 59.2 seconds to play.
But the Wildcats got two free throws from Cheek with 47.8 seconds left to get to within two and Villanova had one more chance with 8.7 seconds to play after Grant missed a three-point shot, and succeeded in forcing the overtime.
The Wildcats shot just under 50 percent in the first half in taking a 39-23 halftime lead. They outrebounded Notre Dame, 24-10, and held the Fighting Irish to 35.7 percent shooting while committing just three turnovers.
Contact staff writer Joe Juliano at 215-854-4494, jjuliano@phillynews.com, or @joejulesinq on Twitter.