The game was the 800th of UH coach Kelvin Sampson's career with his record in 26 season standing at 511-288.
Terry Whisnant led East Carolina (13-18, 6-12) with 13 points.
Houston shot 52 percent in the first half to open a 35-24 lead. With Stiggers scoring 14 of his points in the second half the Cougars steadily pulled way, leading by 21 late.
The Cougars are the 10-seed and face seventh-seeded Tulane on Thursday after eighth-seeded East Carolina meets No. 9 seed Central Florida. The other opening round game is defending national champion UConn, the sixth seed, facing No. 11 South Florida.