Jardine's two free throws gave Syracuse a 64-61 advantage and the teams combined to miss all eight of their field goal attempts the rest of the way.
Josh Gasser brought Wisconsin within a point with 32 seconds remaining by making two free throws, but he was unable to hit a turnaround jumper at the buzzer that would have won it for the Badgers.
Syracuse will take on Ohio State Saturday, with a berth in the NCAA Tournament's Final Four on the line. The Buckeyes eliminated Cincinnati in the second regional semifinal 81-66.
The Orange scored 11 points in a row late in the first half and took a 33-27 advantage at the break. Syracuse held on while shooting 55 percent from the floor and the Orange survived a 3-point barrage from the Badgers.
Long-range shooting accounted for 42 of Wisconsin's 63 points. The Badgers hit 14-of-27 from beyond the arc, but missed their last four tries over the final 6 minutes.
C.J. Fair led Syracuse in scoring with 15 points and Jardine had 14. Dion Waiters added 13 off the bench for the Orange (34-2), whose only two losses this season have come against Big East foes Notre Dame and Cincinnati.
Wisconsin (26-10) was led by 17 points from both Jordan Taylor and Jared Berggren. Taylor hit five 3-pointers and Berggren had three.
Britney Spears debuts 'Perfume' video
Wisconsin business offering 'therapeutic cuddling' forced to close