Michael Washington gave the Razorbacks (12-3) a 74-70 lead by making 1 of 2 free throws with 28 seconds left. Then Quan Prowell missed a 3-pointer at the other end and Beverley added a layup at the end.
The undersized Tigers (9-4) missed four 3s in the final 40 seconds to lose any hope of a comeback.
While Auburn was mostly relying on long-range shots to try to counter a big Arkansas size advantage, Beverley and the Razorbacks were more consistently hitting them.
The Razorbacks shot 58 percent and made 9 of 19 3-pointers. Auburn was 9-of-35 from outside and seldom managed to get the ball around the basket.
Beverley made 5-of-6 3s and scored 12 points in the first half while collecting eight rebounds. Weems did most of his damage in the second half, when he scored 15 points and keyed the run that put Arkansas ahead for good.
He virtually took over after Auburn tied the game at 52-all midway through the second half. Weems, who also had seven assists, scored 10 points to spark a 13-5 run that gave Arkansas a 65-57 lead with 5:54 to play.
Weems added a jumper after Auburn cut the lead to two points, then the Razorbacks hit three straight baskets inside.
Charles Thomas had 14 points for Arkansas on 6-of-7 shots before fouling out.
The Tigers jumped ahead 33-25 midway through the first half then cooled off. They made only one basket over the final 8 minutes. Arkansas scored eight points in a row and tied it up with Gary Ervin's 3-pointer with 2:23 left.
Thomas was called for a foul at the buzzer, and DeWayne Reed made 1-of-2 free throws to cut the Razorbacks' halftime lead to 37-36.