The Gamecocks (5-4) held on even though they had a nearly 6-minute stretch without a field goal late in the second half that allowed the Friars to knock a double-digit deficit all the way down to one.
Weyinmi Efejuku was fouled with 0.2 seconds left on a driving layup and the Friars trailing by two. With a chance to send the game into overtime, Efejuku made only one of two free throws and South Carolina finally escaped with the victory.
Geoff McDermott had 16 points and 10 rebounds for Providence (5-3). The Friars used a 10-minute stretch without a turnover late in the second half to get back in the game.
It helped that South Carolina, which led 54-42 on a Brandis Raley-Ross 3-pointer, went cold from the floor.
Downey, though, ended the drought with a steal and fastbreak layup for a 65-59 lead.
With time running out, the Friars kept chipping away and Brian McKenzie hit a 3-pointer from the top of the arc that made it 67-64 with 33.6 seconds left.
Dwain Williams missed a driving layup and McDermott was fouled after grabbing the loose ball.
McDermott, whose shot nearly fell through the hoop, sank the first three throw with 6.1 seconds left. South Carolina tried to ice him with a timeout, but he swished the second.
South Carolina's Dominique Archie, a former Josey standout, was fouled and he missed the first free throw. He hit the second to make it 68-66 and give the late-arriving crowd there to see the following Villanova game a reason to pay attention in the final 5.1 seconds.
Archie finished with seven rebounds and nine points, with seven of those coming from the free-throw line.
The Gamecocks took advantage of their opportunities from the free-throw line overall. They were 18-for-23 while Providence only went to the line 12 times, making nine.
Philadelphia Eagles cornerback Sheldon Brown, who played at South Carolina and watched from the front row, had to like how the Gamecocks played early.
Raley-Ross and Zam Fredrick hit consecutive 3-pointers midway through the first half to give the Gamecocks a 10-point lead. Downey sank a 3-pointer right before halftime to help South Carolina take a 35-26 lead into the break.