Anthony Elechi scored 13, Brent Arrington added 10 with a career-high 11 assists and Treshaad Williams had 10 for the Eagles (11-9, 5-3 Ohio Valley), who shot 55 percent and outscored the Governors 48-27 in the paint.
Up by five at halftime, Lipscomb pulled away on a 16-2 run and led 46-33 on Williams' dunk with 13:31 to play.
The Governors gained on a 9-2 run, then pulled to within 67-59 on Josh Robinson's 3-pointer with 2:29 left, but got no closer the rest of the way.
Austin Peay's Khalil Davis tied it at 11 with a 3-pointer, but the Eagles pulled ahead on a 9-3 run in which Lamontray Harris hit a 3-pointer and led 28-23 at halftime on 46 percent shooting.
Chris Horton scored 22 and grabbed nine rebounds for Austin Peay (9-14, 2-6), which is 0-3 in conference road games.