COLUMBUS — Backed up to their own goal line, Matt Barkley and Joe McKnight drove into Southern California lore.

Barkley, the freshman quarterback, and McKnight, the shifty tailback, made big play after big play, and Stafon Johnson capped one of the great drives in USC’s storied history with a 2-yard touchdown run with 1:05 left to give the third-ranked Trojans a 18-15 victory against No. 8 Ohio State on Saturday night.

‘‘We’re Trojans. That’s what we do,’’ Barkley said. ‘‘This is what we dreamed of, coming back like this.

‘‘Doesn’t matter where we are in the score. We found a way. I love this.’’

For the Buckeyes (1-1), it was another big-game heartbreaker, maybe the toughest one yet. Ohio State has now lost six straight against top-five teams.

For the Trojans, it was their 10th straight victory against the Big Ten. None was tougher — and none was likely more satisfying for Pete Carroll’s team.

‘‘I think it’s a beautiful statement for our whole team,’’ the coach said. ‘‘It was really a great job by a lot of guys.’’

The official stats will call it a 14-play, 86-yard drive, but it really started with USC at its own 5, facing a second-and-19 with 6:09.

Suddenly, an offense stymied and held scoreless all second half by a hard-charging Ohio State defense came alive.

McKnight darted for 11. Then it was Barkley to McKnight, who weaved for 21 more on third-and-8.

When Barkley threw a strike over the middle to Anthony McCoy for 26 to get USC to the Ohio State 37, the record crowd of more than 106,000 at Ohio Stadium started to grow uneasy.

Barkley converted a fourth-and-short with a sneak. McKnight, so often compared to USC Heisman Trophy winner Reggie Bush, ran three straight times, showing some power to go with all those moves and got USC inside the 10. Another sneak by Barkley got it to first-and-goal.

Then Johnson swept around right end, going in untouched, pointing toward the USC section as he crossed the goal line. It was the only part of the huge crowd cheering. The rest was silent.