Cincinnati (5-5, 4-2 C-USA) opened the season with a win before losing five of its next six games and falling into a tie for last place. But the Bearcats have bounced back to win three straight and need to win two of their last three to reach their school-record third consecutive both game.
Guidugli completed 14 of 23 passes for 238 yards, becoming the third quarterback in school history to reach 5,000 career passing yards. He is the quickest quarterback to reach the milestone.
Houston had a 7-3 lead before Guidugli capped an 80-yard drive with a 10-yard touchdown run to give Cincinnati the lead for good.
Guidugli threw a six-yard touchdown pass to Jon Olinger late in the first quarter and connected with LaDaris Vann on a six-yard scoring strike midway through the second for a 24-7 cushion.
Bearcats defensive end Antwan Peek extended the lead with 4:05 left in the first half, when he returned a fumble 21 yards for his second touchdown in as many games.
DeMarco McClesky rushed for 83 yards on 16 carries as Cincinnati gained 205 of its 492 yards on the ground.
The Bearcats, who limited Louisville to just 176 yards last week, held the Cougars to 293, including 92 rushing.
Nick Eddy completed 10 of 23 passes for 152 yards and three interceptions as Houston (4-6, 2-5) lost for the fifth time in seven games.