Tied at halftime, Lawrence scored the go-ahead free throw, 67-66, with 42 seconds left to spark an 8-0 run and the Bison (9-5, 1-0) pulled away.
Dexter Werner scored 13 and the Bison shot 11 of 22 from distance.
The Bison led 21-6 after free throws by Alexander, but Oral Roberts rallied 21-3 to lead 34-29. The Bison used a 5-0 run to tie it at 34 at halftime.
Oral Roberts led 41-36 on a 3-pointer by Obi Emegano early in the second half, but Alexander hit back-to-back 3s and the Bison led 42-41. The lead traded hands nine more times before Alexander's go-ahead free throw.
Emegano scored 25 for Oral Roberts (6-8, 0-1), Henderson had 17 and Korey Billbury 13.