The quarterback established a new single-game school mark for touchdowns in Saturday's 77-10 victory against Bowling Green, throwing for six scores and rushing for another to break a record he previously shared with two others.
The Buckeyes also shattered a school record with 776 yards, breaking the old mark of 718 set in 1930 against Mount Union.
"It's one game," said a subdued Ohio State coach Urban Meyer said. "Let's chat in about four weeks and see how we're doing."
Barrett, who set the Big Ten record for touchdowns with 45 during his breakout freshman campaign two years ago, threw for 349 yards on 21-of-31 passing as the Buckeyes opened up the season with a rout of the Falcons at Ohio Stadium.
Now unquestionably the leader for Ohio State after a trying 2015 season in which he split time with Cardale Jones, Barrett carved up Bowling Green seemingly at will before being relieved midway through the third quarter.
His day actually got off to a rocky start, making an ill-advised throw into coverage in the first quarter that was returned for a touchdown that put Ohio State in an early hole. But Barrett -- healthy for the first time during spring practice and training camp -- bounced back in a big way, breaking a three-way tie for the school mark.
Barrett also posted six TDs in 2014, matching a feat accomplished by former Buckeyes Kenny Guiton and Tony Curcillo.
The Associated Press contributed to this report.