Alex Lyons returned a blocked field goal 61 yards for a touchdown with 2:19 to go in the game to get Rice close, but the Owls missed on the two-point conversion.
Rice recovered the ensuing onside kick at its 47-yard line but was unable to score.
Deontay Greenberry and Ryan Jackson each caught a touchdown in the second half to help lead the Cougars (3-0).
Greenberry finished with 146 yards receiving on six catches, including a 61-yarder from O'Korn in the first quarter to set up Houston's first score.
Jackson, who tallied 57 yards receiving, also rushed for 87 and a touchdown on 19 carries.
Senior Taylor McHargue went 21-for-36 for 232 yards with an interception, and Turner Peterson finished with 102 yards and a touchdown on five catches for the Owls (1-2).
McHargue's 1-yard sneak for a touchdown with 10:52 left in the fourth got Rice within 11.
Houston improved to 29-11 all-time against crosstown rival Rice.
The game, held before 34,831 at Reliant Stadium, home to the NFL's Houston Texans, marked the first time since 2003 that the schools met as members of different conferences.
Houston's joined the American Athletic Conference this year while Rice remained in Conference USA.
Rice's Chris Boswell had an extra-point attempt blocked in the first quarter and missed field-goal attempts of 55 and 50 yards in the second and fourth quarters, respectively.
O'Korn was making his first start of the season, replacing junior David Piland.
Piland, who did not practice during the Cougars' bye week, sustained a concussion in the first quarter at Temple on Sept. 7. O'Korn came in to lead the Cougars to a 22-13 win.
Houston trailed 13-7 after an error-laden first quarter, which saw O'Korn throw his first interception of the season and free safety Trevon Stewart commit a costly roughing-the-kicker penalty that set up Rice's first score.
Rice quarterback Luke Turner connected with Turner Peterson for a 57-yard TD pass to put the Owls on the board, 6-0, with 12:57 to go in the first quarter, but Boswell had the extra-point attempt blocked by B.J. Singleton.
It didn't take long for Houston to answer.
On the third play of the ensuing drive, O'Korn found Greenberry for a 61-yard pass to set up Jackson's 1-yard run. Leone Richie booted the extra point to put the Cougars ahead 7-6.
Rice came roaring back, however, with McHargue finding an alone Klein Kubiak on third-and-6 for a 29-yard pass. Kubiak was forced out at the Houston 1, but the pass set up Charles Ross' 1-yard TD rush up to middle to give the Owls the 13-7 lead with 11:25 to go in the first.
O'Korn exited the game briefly with under 6:50 left in the first after a hurry by Michael Kutzler left him lying on the ground for a couple of minutes. He was replaced by freshman quarterback Greg Ward Jr.
Ward, who saw action after O'Korn's return, went 3-for-3 for 48 yards and rushed nine times for 80, including a 29-yard run in the second quarter to set up a Houston field goal.
