Leonard scored the Bears final seven points, rallying them from a 67-62 deficit with three minutes to play.
Ronshad Shabazz hit a 3-pointer with :41 left to give the Mountaineers a 70-67 lead, but Leonard, who finished with 23 points, got to the basket twice for layups in the final :15.
Mercer (5-1) bounced back after losing its first game of the season Monday at Davidson, 77-71 by shooting 51 percent from the field against the Mountaineers, converting 25 of 49 field goal attempts.
Frank Eaves equaled his career-high with a 31-point performance for Appalachian State (2-4). Chris Burgess and Tyrell Johnson added 12 and 11 points, respectively. Appalachian State shot 24 of 52 from the field (46.2 percent), including 13 of 29 from distance.