Davidson (21-6, 12-4 Atlantic 10) took its largest lead of the game at 67-51 after a 9-0 run capped by Jordan Barham's three-point play with 6:13 to go.
George Washington answered with 10 straight points to get within six at 3:56, but the Colonials (18-11, 8-8) got no closer.
Barham finished with 17 points and Tyler Kalinoski added 11.
Davidson entered the night in a four-way tie with Dayton, Rhode Island and No. 22 Virginia Commonwealth. Rhode Island won, and Dayton's 59-55 victory over VCU knocked the Rams out of the first-place knot.
The Wildcats led 32-30 at halftime but never trailed in the second.