The bench played a big role in the victory for the Mustangs (21-6, 10-4 American Athletic Conference), scoring 31 points and grabbing 21 rebounds. Cunningham had six points and six boards.
SMU broke a tie at 39 early in the second half to take the lead for good but didn't shake Houston until the final minutes. SMU led by five points with 56 seconds to play before four free throws by Nic Moore and Ben Moore pushed its lead to nine with 19 seconds left.
SMU has already won more games this season than any SMU team since the 1999-00 season. SMU, seeking to earn its first berth to the NCAA Tournament since 1993, is third in the conference standings.
They've won all 14 home games this season - the first six played off campus while 57-year-old Moody Coliseum was undergoing a $47 million renovation - to build the program's longest home winning streak since 1984-85.
The Cougars have lost seven of their last eight games and nine of their last 11.
The Mustangs trailed for most of the first half, thanks early on to Houston's accuracy on 3-point shots. House sank three of his first four attempts from behind in the arc during the opening five minutes, and Houston used four 3-pointers in build a 14-6 lead.
SMU's Markus Kennedy, averaging 12 points per game, being benched at that same time for the balance of the half after picking up two fouls.
The Mustangs slowly fought back on the strength of its bench play to grab a 32-30 lead at intermission. SMU reserves outscored Houston's 18-8, led by Cunningham.
Thomas, the Cougars leading scorer at 16 points per game, was limited to one field goal and five points in the first half.