But it didn't do so without a fight from the upset-minded Bears, who pulled off the shocker last year in Waco but were unable to accomplish that feat this time around.
On a blustery day, Baylor hung around until midway through the fourth quarter when the Belldozer Blake Bell busted loose 55 yards to the house for a 42-26 advantage at the time that OU would ultimately milk to the end.
Because of that, Stoops has moved into second all-time in OU career wins with 146, surpassing legendary Sooner coach Bud Wilkinson.
The Sooners quickly got on the board first when they, for just the third time all year, scored an opening drive touchdown.
Baylor came back with an impressive 58-yard field goal from place kicker Aaron Jones, but it didn't take long for the Sooners to march down the field again.
Clay, responsible for his third touchdown in as many quarters, galloped in from one yard out to make it 14-3.
Teams traded scores the rest of the way in the first half.
First it was quarterback Nick Florence and the Baylor offense that moved 80 yards in just six plays, capped off by his 5-yard touchdown run for 14-10 score early in the second.
Then, Sooner running back Damien Williams answered with his first touchdown in three weeks as he sprinted in three yards to pay dirt.
Just 32 seconds before the half, Bears running back Lache Seastrunk continued the back-and-forth exchange with a 4-yard score of his own.
But Clay's 36-yard kickoff return moments later set OU up for the final score of the first half and a double-digit lead at intermission.
Jones and wide receiver Justin Brown connected on a 35-yard touchdown toss with 15 ticks to go.
Coming out of the gates in the second half, Jones converted a 21-yard field goal to trim the deficit to 28-20.
Williams then put it on the turf and, when OU got the ball back on downs, Jones threw a terrible ball along the nearside boundary that Baylor safety Mike Hicks picked off.
That set up Seastrunk for his second touchdown of the contest, a 2-yard rush to draw Baylor within two.
However, the two-point try failed, and OU responded with a statement drive.
A trip that spanned 10 plays and 75 yards resulted in Williams' second score, a 17-yarder, and a 35-26 advantage.
OU extended it to a 16-point lead when the Belldozer cruised 55 yards on third-and-1 to paint early in the fourth.
The Bears capped off the scoring when Seastrunk notched his third touchdown, a 6-yard run, in garbage time, and Florence rushed for the 2-point conversion.
Jones finished 25-of-36 for 278 yards and two touchdowns with the one pick, while Williams took the bulk of the carries again and gained 98 yards and a score on the 23 rushes.
Brown led all Sooner receivers with his six catches for 83 yards and a touchdown.
For Baylor, Florence, the nation's No. 3 passer coming into the contest, was just 12-for-33 for 172 yards without a touchdown through the air for the first time all year.
He did lead the Bears rushing attack with his 94 yards and a touchdown on 12 carries, While Seastrunk's trio of scores came while netting 91 yards on 15 runs.
Baylor's Terrance Williams had six catches for 91 yards to pace the receiving attack.
OU now heads into its first ever Big 12 Conference matchup in Morgantown, W.V., against the West Virginia Mountaineers at 6 p.m. CT Saturday, while Baylor returns home to face undefeated Kansas State at 7 pm. CT.