Russell matched a school record with six touchdown passes, three of his five in the first half to Corey Coleman, and the Bears wrapped up their non-conference schedule with a 70-17 romp over Rice on Saturday.
The Bears (3-0) extended the nation's longest home winning streak to 18 games, including the first eight at their campus stadium in the Brazos River. They were coming off a bye following sluggish starts in victories against SMU, a one-win team last year, and lower-division Lamar.
Coach Art Briles blamed himself last week for the Bears lacking the intensity that helped carry them to a pair of league titles. Now he gets a little help from the schedule with the Big 12 opener against Texas Tech coming next Saturday at the home of the Dallas Cowboys.
"Instead of kind of being the hunted so much, it kind of equals out when you get into conference play because we're all playing for those glass trophies that I've got sitting in my office," Briles said. "We're all playing for the same thing. We've got a little bit of hunt in us coming this week."
The Owls (2-2) lost their 25th straight game against a Top 25 opponent, a streak that goes back to 1997.
Russell threw for 277 yards and Shock Linwood ran for 158 with a touchdown as the Bears rolled up more than 700 yards for the third straight game -- a season-high 793 this time.
The national leader in yards and points per game coming in, Baylor scored at least 70 for the sixth time since 2013 and reached 60 for the 15th time in five seasons -- six more than any other FBS school.
"We work to be perfect in everything we do," said Russell, who had the six scoring tosses on just 12 completions without an interception after throwing three against Lamar. "We're not going to be perfect, but that's something that we really strive for each day in practice."
Rice was within 14-10 midway through the first quarter before Baylor scored 28 straight points for a 42-10 halftime lead. Coleman had three of the four half-closing scores.
The Bears sacked Rice quarterback Driphus Jackson five times -- four in the first half, including the 15th of Shawn Oakman's career to tie a school record. Jackson had 115 yards passing and one touchdown a week after throwing for 373 yards and three scores in a win over North Texas.
Rice had three different 100-yard rushers the first three weeks, but just 32 yards on 12 carries from leading rusher Jowan Davis against Baylor as the Owls averaged 2.1 yards per carry.
"They were as advertised," Jackson said. "It wasn't anything they do that we're not familiar with. But we just got beat physically."
The Bears finished with 427 yards rushing -- 55 shy of the 22-year-old school record. Terence Williams had 111 yards and the final Baylor touchdown.
Jackson's fumble near midfield with the Owls trailing 14-10 -- forced and recovered by safety Orion Stewart -- led to Russell's first scoring pass to Coleman from 16 yards. Coleman had 100 yards receiving.
After Linwood's 11-yard touchdown run, Coleman made a leaping catch over safety J.T. Ibe at the goal line for a 35-yard score. He caught a short pass in front of cornerback V.J. Banks and faked inside before beating him to the sideline on a 32-yard touchdown.
Russell tied the school record for scoring passes on a 22-yarder to Lynx Hawthorne on his final series of the game in the third quarter. He shares the mark with Blake Szymanski (2007 against Rice) and Bryce Petty (2013 against TCU).
"The touchdowns, it comes with the game," Russell said. "And that's something that we really pride ourselves on is throwing the ball deep and getting points."