Saturday's narrow decision also marked a milestone for Orange head coach Jim Boeheim, who earned his 400th career Big East conference win.
Fab Melo added 11 points and nine rebounds for Syracuse (29-1, 16-1 Big East), including the go-ahead dunk in the final minute to lift the Orange to their ninth straight win.
Syracuse held a 43-29 advantage at the break and Joseph opened the second half with a three-pointer to give the Orange their largest lead of the game, but Connecticut would not go quietly.
The Huskies started their comeback attempt with a 17-8 run to close the gap to 54-46 with 13:29 left in the game.
A pair of Joseph free throws followed by a Scoop Jardine layup extended Syracuse's lead back to 11 before the Huskies reeled off a 14-3 swing to knot the game at 63 on Drummond's layup with 4:18 remaining in the contest.
Connecticut would not take the lead, though, as back-to-back layups by Joseph and Melo put the Orange back on top.
The Huskies battled back to tie the game at 69 with 47 seconds left when Roscoe Smith followed up a Ryan Boatright miss with a tip-in, but Melo's put- back slam on the other end made it a 71-69 contest with half a minute remaining in the game.
Boatright's three-point attempt on Connecticut's ensuing possession was partially blocked by Dion Waiters, but the loose ball was deflected out of bounds by Syracuse with 13.3 seconds showing on the clock.
Then, coming out of a timeout, Smith's off-balance shot while being harassed in the lane was turned aside by C.J. Fair to seal the victory for Syracuse.
After Drummond's dunk gave the Huskies a 6-5 lead three minutes into the first half, Connecticut would never have the lead again, as the Orange answered with a 20-5 run to jump out to a 25-10 lead and take control of the game.
Connecticut trailed by at least nine for the remainder of the half as they shot just 36.7 percent from the floor en route to a 43-29 deficit at the half.
Syracuse leads the all-time series, 53-36...The Orange improved to 9-1 on the road this season, including an 8-1 mark in Big East road contests...UConn fell to 12-4 at home and 4-4 in Big East home games...Connecticut head coach Jim Calhoun missed his seventh straight game with a worsening spinal stenosis, a lower back condition. He has missed 28 games in his 26-year tenure as the Huskies' coach. UConn is 14-14 in those contests.