The Wildcats (12-7, 3-3 Big East) led by as many as 10 points in the first half and rallied late in the second to send the Cardinals to their second straight loss. Louisville (16-3, 4-2) had an 11-game winning streak end in a 70-68 loss to Syracuse on Saturday.
Ryan Arcidiacono scored 15 points, and JayVaughn Pinkston and Mouphtaou Yarou each scored 11 for Villanova.
The Wildcats students packed behind each basket stormed the court in a wild celebration for a win coach Jay Wright's struggling program badly needed.
Yacoubou hit the go-ahead 3 with just less than 4 minutes left and the Wildcats held on from there.
Peyton Siva had 15 points and 13 assists for the Cardinals and Wayne Blackshear scored 17 points. The Cardinals didn't play like a team that was just the No. 1 team in the country. The Cardinals, a 71 percent free throw shooting team, was 12 of 24 from the line and shot 40 percent from the field.
Wright's program has fallen from among the Big East's elite following a run to the 2009 Final Four. The Wildcats were eliminated on the first weekend each of the next two tournaments and failed to qualify last season for the first time since 2004. The Wildcats needed this one.
Darrun Hilliard of the Wildcats picked off a pass at halfcourt and was fouled on the driving, crashing layup. He made the free throw to cut it to three. Yarou stepped back for the jumper to make it a one-point game. Pinkston tipped in the go-ahead basket for a 53-52 lead.
The Cardinals missed five straight from the free throw line (including two front ends of 1-and-1s) to keep Villanova's simmering upset hopes alive. Chane Behanan hit one to end the streak and tie the game at 53-all.
Yacoubou snapped the tie with a baseline 3 in front of Villanova's bench that sent his teammates into a frenzy. James Bell followed with another 3-pointer for a six-point lead and the upset win only 2:50 away.
Behanan fumbled the ball along the baseline and the Wildcats pounced. Arcidiacono was fouled and made two free throws for a 62-55 lead.
The Wildcats used to routinely pack the Wells Fargo Center, home of the NBA's 76ers, for their biggest Big East games. Not even the No. 5 team in the AP poll was much of an attraction on Tuesday. Most of the upper deck was empty and the lower bowl had plenty of good seats available. When No. 3 Syracuse visits Saturday, the arena could be full of orange.
The Wildcats didn't need much of a crowd to make a run at an upset in the first 20 minutes. They hit their first four 3-pointers, beat the Cardinals on the boards, and hustled for every loose ball with the desire Wright would expect in a big game.
They built a 10-point lead that was erased by Louisville's 12-0 run. The Cardinals made the bulk of that run without Siva, who left after a hard full around the basket. Pinkston ended a 4½-minute scoring drought with a three-point play and he scored the final basket of the half for a 30-28 lead.