Vintavious Cooper rushed for 140 yards and a touchdown for the Pirates (6-4, 5-1 Conference USA), who posted their highest point total this season.
The victory makes East Carolina bowl-eligible for the sixth time in the past seven seasons.
Carden's 31 completions and 43 passes are both career highs. He has thrown 16 TD passes against seven interceptions this season. Danny Webster caught six of Carden's passes, three of them for TDs.
The Pirates outgained the Cougars (4-5, 3-2) 245 to 28 yards rushing, which contributed to their nearly 30-minute advantage in time of possession. Houston ran the ball only 11 times.
Houston's David Piland threw 51 passes, completing only 22, including four for touchdowns. He and Carden threw one interception each.