With the win, the Indians improved to 3-1 overall and 2-0 in the American Southwest Conference West Division. The Comets, meanwhile, dropped to 1-3 and 0-2.
Qualls scored all of his team's points with nine straight during a 1 minute, 43 second span in the first half to set the stage for McMurry's first lead of 20-19 on a pair of J.R. Williams free throws with 5:06 left. But UTD came back to lead 30-27 at the break.
Then in the second half, Qualls gave the Indians the lead for good at 48-47 on a 3-pointer at the 9:25 mark and converted a four-point play at 7:34 to give them their biggest cushion at the time of eight points, 55-47.
UTD's Jason Malone led all players with 22 points.
In addition to Qualls, Terence Mirabal (14 points), Cole Dickerson (12) and Williams (10) also scored in double figures for the Indians.
McMurry sophomore post Travis Tennison, who averages a double-double with 17.7 points and 11.0 rebounds per game, was forced to sit out tonight's game and serve an ASC-imposed one-game suspension after being ejected while picking up two technical fouls during Saturday's win versus Texas-Tyler.
But the Indians still led the Comets in rebounding (34-32) and blocked shots (4-0).