Memphis closed the game on an 8-0 run in the final 3:30, with four points apiece from Nichols and Nick King.
King and Trahson Burrell each added 11 points as the Tigers (13-7, 6-3 American) shot 53.8 percent. King also grabbed seven rebounds and Burrell had three blocks.
Terry Whisnant had 17 points, shooting 5 of 7 from 3, and Caleb White pitched in 10 for East Carolina (8-12, 1-6). The Pirates lost their team-leading rebounder (5.8 per game), Michel-Ofik Nzege, to a head injury in the first half.
Memphis started the game on a 24-9 spurt and built a 39-24 halftime lead.
East Carolina began the second half on a 16-6 run, including three 3-pointers. Later, the Pirates cut the lead to four, 62-58, with 3:50 left, but wouldn't score again.