Moore and Smith each made four 3-pointers and Winthrop shot 55.6 (10-18) from beyond the arc.
Reinhardt opened with back-to-back 3-pointers for a 6-2 lead, but Josh Davenport hit a jumper, sparking a 16-2 run and Winthrop led 44-32 at halftime.
Winthrop had a 14-point lead, 54-40, on a layup by Smith, then led 87-62 after Moore hit back-to-back 3-pointers. The Eagles reached the 100-point mark on Duby Okeke's jumper with 44 seconds to play.
Corey Ricks led Reinhardt (1-5) with 21 points, Perie Finley scored 12, Matt Porter 11, and Justin Zachary 10.