Jardine had 20 points and six assists for the Orange (23-6, 10-6), while Jackson had 18 points, five rebounds and four blocks.
The win was the sixth this season over a ranked team for Syracuse, tying it with No. 5 Texas for the most in the nation.
The teams swapped road wins, with Villanova winning 83-72 at Syracuse on Jan. 22.
Corey Stokes returned from missing three games because of a turf toe injury to lead the Wildcats (21-7, 9-6) with 24 points, including matching his season high with five 3-pointers.
But it was at the free throw line where the teams traded places.
Villanova, which entered the game leading the Big East in free throw shooting at 76.8 percent, was 17 of 27 at the line. Stokes, third in the nation at 93.5 percent, went 5 of 8.
Syracuse, last in the 16-team Big East at 65.5 percent, went 13 of 17 from the line, a performance topped off by freshman Dion Waiters making two with 14.1 seconds left for a 67-64 lead, and Jackson making two - the second a bank shot - with 4.6 seconds to go for the final margin.
Corey Fisher, coming off a career-high 34 points in Villanova's overtime win at DePaul on Saturday, finished with eight points on 3-of-16 shooting, including missing all eight of his 3-point attempts. Maalik Wayns had four points on 1-of-9 shooting and missed all three of his 3-point attempts.
Syracuse took a 55-47 lead with 9:05 to play on two free throws by Jackson.
Villanova went on a 9-2 run - five points by Stokes - to get within 57-56 with 5:28 to play.
Jardine made a free throw and a 3 to make it a five-point game.
The Wildcats were able to get within one two more times, the second at 65-64 on two free throws by Isaiah Armwood with 21.7 seconds to go.
Waiters and Jackson sandwiched their clinching free throws around a turnover by Villanova.
Brandon Triche had 11 points and seven rebounds for the Orange, who shot 47.3 percent for the game (26 of 55).
Armwood had 12 points and 10 rebounds and Antonio Pena had seven points and 10 rebounds for the Wildcats, who shot 32.2 percent (21 for 65) for the game and 5 of 26 on 3s (19.2 percent).
The last 30 seconds of the first half went as badly as it could for Syracuse.
The Orange had a 29-22 lead and Jardine was walking the ball down court, apparently ready to run some time off the clock.
His pass to the right wing was intercepted by Wayns, who went in for a layup and was fouled by Jardine, his third. Wayns missed the free throw but the Wildcats got the rebound. Fisher missed a 3 but Armwood grabbed the rebound and was fouled by Kris Joseph, his third.
Armwood made the first and missed the second but Triche was called for a lane violation. Armwood missed but again Triche was called for another lane violation. As the refs were signaling the play, Syracuse's Baye Moussa Keita was called for a technical foul.
Stokes made one of two on the technical and Armwood finally made his second.
The half ended with Syracuse up just 29-27.