Campbell, who scored 14 points in the first half, tied the rebound mark set by former Blazer Carlos Williams against Grambling State in December 1996.
P.J. Arnold added 13 points for UAB (11-9, 4-4 Conference USA).
Chad Hendrick led the scoring for Houston (4-15, 1-6) with 18 points. Patrick Okafor had 11 rebounds.
The Blazers, who led the entire second half, outshot Houston 43 percent to 38 percent. The Blazers outrebounded Houston 44-32.
The Cougars cut the lead to two points at with 14:48 remaining, making the score 38-36. But UAB responded with six straight points.
UAB would eventually lead by 13 points, 62-49, with 1:52 remaining.
UAB scored 34 points off of turnovers compared to Houston's 17.
UAB's David Walker injured his hand on a fall midway through the first half but later returned to the game, scoring seven of
his nine points in the second half.