Keenum -- the NCAA's all-time leader in passing yardage and TD tosses -- wrapped up his collegiate career by going 45-of-69 through the air for Houston (13-1).
Patrick Edwards made nine grabs for 228 yards with two touchdowns as the Cougars improved to 2-9 in their last 11 bowl games.
Tony Levine earned a victory in his head coaching debut after replacing the departing Kevin Sumlin.
The Nittany Lions (9-4) got a shaky performance from Rob Bolden, who completed only 7-of-26 passes for 137 yards while replacing injured starter Matt McGloin.
McGloin missed the game after suffering a concussion during an altercation with a teammate last month.
Interim head Coach Tom Bradley guided the Nittany Lions to a 1-3 record.