K.J. McDaniels notched his seventh game this season with double-figure points and rebounds for Clemson, while Rod Hall scored 16 points, 10 of those coming in the two overtimes.
Allen's final basket gave the Terrapins a 71-70 lead with 1:27 to go. That's when McDaniels drove the lane and found Harrison open in the right corner for his only long-range basket of the game. Smotrycz had 19 points off four 3-pointers for Maryland.
The Tigers seemed to wrap it up on Hall's 3-pointer with 19.2 seconds left in the first overtime for a 63-59 lead. But officials reviewed the shot, found his feet were on the line and changed it to a two-point goal and a 62-59 lead. That's when Smotrycz hit his fourth 3-pointer with 7.6 seconds to go and tied things once more.
McDaniels got the ball to the rim on Clemson's last possession, but it fell away and brought a second extra period.
Maryland appeared in good shape after a 14-5 run early in the second half to move in front 48-44. The Terps were still up 54-50 on Allen's bucket with 5:02 go, but they did not score after that and missed their final eight shots of the half.
Clemson didn't do much better, but tied the game on Jaron Blossomgame's three-point play with 3:24 left and McDaniels' foul shot a minute later.
Clemson got the final chance with 7.3 seconds left, but Adonis Filer's running shot bounced away at the horn.
Maryland seemed to find its stride after that with an 11-1 run — Allen had seven points and Charles Mitchell four — to grab a 27-18 lead with 4:46 left.