The Tigers forced a Gradnigo miss with 8 seconds remaining, but guard Anthony Raffa swooped into the lane to grab the offensive rebound and give the Chanticleers (5-0) another chance.
After a pair of timeouts, Gradnigo missed a leaning jumper from the foul line. But his defender, Bryan Narcisse, fell down backward on the shot, leaving a clear path for Grandigo to get the two-handed tip and finish off the Chanticleers' rally from a 10-point deficit.
Gradnigo finished with 21 points, 15 coming in the second half.
Andre Young had 20 points for the Tigers (2-2), who suffered their second straight defeat to an in-state mid-major after falling 72-69 at College of Charleston on Saturday.
Clemson shot 40.3 percent (23 of 57) and didn't have another scorer in double figures, yet the Tigers held a four-point lead with 1:41 left on Tanner Smith's 3-pointer from the right corner.
Coastal Carolina manufactured its comeback by spreading the perimeter against Clemson, and with 59 seconds left, Gradnigo had an arching 3 bounce high off the rim and in to pull the Chanticleers back within one.
The Chanticleers, who at one point were down by 10, 37-27 with 18:28 remaining, scored two baskets off of turnovers to go up 41-40 with 12:17 remaining.
From there, the lead by either team was no greater than four points, as Coastal Carolina shot 63.6 percent from the field in the second half (14 of 22).
Coastal Carolina won in the return of its coach Cliff Ellis, who was the head man at Clemson from 1984-89.
Ellis was honored at the start of the game with a plaque, before getting on his knees and kissing the orange paw at center court before tip-off.