Malcolm Kelly caught three of Bradford's TD passes and Reggie Smith returned a fumble for a score as the No. 5 Sooners rolled over Miami 51-13 in their first meeting since the Hurricanes swept three games in the 1980s.
"That didn't matter," Oklahoma coach Bob Stoops said. "It makes for a good story, but that's a long time ago."
Bradford completed 19-of-25 passes for 205 yards in his second career start as the Sooners (2-0) evened the all-time series at three games each. All three of Oklahoma's losses came in a three-year span when the Sooners went 33-0 against all opponents except the Hurricanes.
Stoops said he introduced his players to the rivalry's history on Monday, but after that "they're rolling their eyes. That's 20-some years ago. Most of them weren't even born."
Stoops said even he had a hard time going back that far, but he hoped the win was a lift for Sooners fans who had been "storing those hard feelings all those years."
"I can't say I thought a lot about that," said Bradford, who wasn't even two months old when the last Miami-Oklahoma game was played. "I was really trying to play for today."
Oklahoma built a 21-3 first-half lead on Bradford's touchdown passes of 23 and 24 yards to Kelly and Smith's 61-yard return of a Javarris James fumble, the third-longest fumble return in Sooners' history.
Neither starter Kirby Freeman nor backup Kyle Wright could mount enough of a comeback, and Miami (1-1) suffered its most lopsided defeat since a 66-13 loss to Syracuse on Nov. 28, 1998.
"Today wasn't a very good day for the University of Miami," said first-year coach Randy Shannon, who was a linebacker on the Miami teams of the mid-1980s. "The guys have to understand that when you come up to an opponent like the University of Oklahoma, they are a very great team and have a lot of talent just like we have a lot of talent."
Under Freeman's guidance, Miami settled for a field goal after getting a first-and-goal at the 8-yard line following Oklahoma sophomore Derek Shaw's snap over punter Michael Cohen's head. Through seven offensive drives, Freeman completed only two passes for 10 yards and Miami had only one first down.
That's when Shannon made a change.
Wright, who split starts with Freeman last season, led an 18-play, 52-yard scoring drive that was extended by a fake field goal and two pass interference penalties in the end zone. Wright finished it with a 6-yard touchdown pass to Ryan Hill to pull Miami within 21-10 before the half.
The Hurricanes had a chance to cut into the deficit even more after Chris Brown fumbled on Oklahoma's opening second-half drive, but again settled for a Francesco Zampogna field goal.
Miami finished with 139 total yards and seven first downs.
"As a team, we want to go out and win every game like everybody else does. But we think on a consistent basis, we can come out and show something to the nation and we'll take each week as a stepping stone," Sooners safety D.J. Wolfe said.
Sparked by Juaquin Iglesias' 43-yard second-half kickoff return, Oklahoma responded immediately on a shortened field and tight end Jermaine Gresham caught Bradford's third touchdown pass. Bradford and Kelly hooked up again for a 30-yard scoring strike, with Kelly making an over-the-shoulder reception, to make it 38-13 early in the fourth quarter. Kelly finished with 102 yards receiving on four catches.
Bradford then added a 9-yard TD pass to fullback Dane Zaslaw to match the school record set by 2003 Heisman winner Jason White and 2000 Heisman runner-up Josh Heupel. Last week, Bradford broke Heupel's record for yards in a half and tied White's mark with 18 straight completions.
"I'm really not surprised," Bradford said. "Knowing the guys that are out there with me, I can't explain it. It's unreal how good those guys out there are."
Following a 79-10 win against North Texas in the opener, Oklahoma is averaging 60 points per game.
"From the beginning, we've known that this offense has a lot of capability. We have a lot of potential," Bradford said. "We know if we go out there and we play hard and we play smart that we definitely have chances to be a great offense."
Wright was 7-for-14 for 65 yards. Freeman, who returned late in the third quarter, was 3-for-9 for 17 yards. James and Graig Cooper, who combined for 215 yards rushing in a 31-3 win against Marshall last week, were held to 54 yards.