Updated

James Conner did his normal yardage-churning, defender-punishing work on the ground. It wasn't enough for Pittsburgh to earn a road win and get closer to bowl eligibility.

The Atlantic Coast Conference's leading rusher ran for 220 yards and four touchdowns, his second straight game with at least 200 yards, in Saturday's 40-35 loss at North Carolina. Along the way, Conner set ACC and program records for most season rushing yards by a sophomore.

Conner scored from 56 yards out on the game's first possession, then added scoring runs of 16 and 2 yards. On his last TD, he broke four tackles and dragged two defenders the final few yards for a 22-yard score that gave Pitt a 35-34 lead with 3:33 left.

"You appreciate that," Pitt coach Paul Chryst said of Conner's performances. "I think it is almost arrogant to expect it out of someone."

Conner has now run for 1,562 yards and a league-record tying 21 touchdowns this season with two games still to play.

"We knew coming into this game that those guys could run the football," UNC coach Larry Fedora said. "Nobody has stopped them and we didn't stop them today."

Unfortunately for Conner, UNC's T.J. Logan scored from 1 yard out with 50 seconds left to earn the win.

Logan's short scoring run capped a 75-yard drive and marked his second go-ahead touchdown in the final minute of a game this season for the Tar Heels (5-5, 3-3).

The Panthers (4-6, 2-4) had a final chance, but quarterback Chad Voytik fumbled on a hard hit from Malik Simmons near midfield. Shakeel Rashad grabbed the loose ball with 15 seconds left to secure the win.

Marquise Williams turned in a huge performance for UNC, which trailed 14-0 before getting its offense rolling. Williams ran for 122 yards and three touchdowns, and also threw for 276 yards and a score.

Conner's last score put the Tar Heels in the same position they were a month earlier — down late but with the ball.

In the last home game, Georgia Tech went ahead on a 75-yard reverse with 3:07 left, before Williams led the go-ahead drive for the winning score with 11 seconds to go.

Logan had the winner there, too, scoring from 2 yards out for the 48-43 win on Oct. 18.

The teams entered this one in the same position, each needing two wins in the final three games to become bowl eligible. Now the Tar Heels are a win closer while the Panthers must beat both Syracuse and Miami to get there.

Tyler Boyd also had a big day for Pitt, catching five passes for 160 yards and a 50-yard score midway through the second quarter.

Ryan Switzer scored on a 63-yard catch-and-run touchdown early in the third quarter for the Tar Heels, while Logan finished with 92 yards rushing.

The teams each cracked the 500-yard mark and combined for 1,025 total yards of offense.

North Carolina played without tailback Romar Morris, who was suspended one game after a recent DWI arrest. The Tar Heels were also without linebacker Travis Hughes due to an unspecified violation of team policy.

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Follow Aaron Beard on Twitter at http://www.twitter.com/aaronbeardap