Conner broke a Pittsburgh bowl record for yards rushing held by Tony Dorsett, and Chris Blewitt kicked a tiebreaking field goal with 1:17 remaining.
Conner even played a handful of snaps on the defensive line. Boyd gave Pitt (7-6) a boost with his versatility as well.
One star the Panthers will have to replace is Aaron Donald, their All-American on the defensive line.
Donald, a senior, helped thwart any last-ditch comeback with a sack deep in Bowling Green territory in the final minute.
"They were without question the most physical team we faced all season," said Adam Scheier, Bowling Green's interim coach. "The offensive line was tough, the running back was obviously a bear to tackle and the whole defensive line was disruptive. We knew we had to keep Donald and their other guys out of our backfield, but we couldn't do it."
Scheier took over after Wake Forest hired coach Dave Clawson away from the Falcons. Scheier coached the bowl, but now Dino Babers takes over.
Dorsett rushed for 202 yards in Pitt's win over Georgia in the Sugar Bowl on Jan. 1, 1977. The school's receiving record for a bowl came the next season. In a Gator Bowl win over Clemson, Gordon Jones had 163 yards receiving.
Both marks fell Thursday.
The 6-foot-2, 230-pound Conner rushed for 165 yards in the second half, helping Pitt overcome the loss of quarterback Tom Savage, who didn't play after halftime because of a rib injury. Conner and the Panthers drove 51 yards in seven plays late in the fourth quarter to set up a 39-yard kick by Blewitt, who had missed from the same distance earlier.
Then Conner was back on the field on defense, helping the Panthers protect the lead.
"After the last game, coach told me they wanted to unleash me on both sides of the ball, so I've been getting a lot of reps both ways," Conner said. "I was pretty tired by the end, but I wasn't going to tap out. They kept giving me the ball, so I just kept running."
Chad Voytik relieved Savage and put Pitt ahead 27-20 with a 5-yard touchdown run in the fourth quarter, but the Falcons who upset Northern Illinois in Detroit in the Mid-American Conference title game earlier this month tied it on Matt Johnson's 15-yard strike to Ryan Burbrink with 4:42 to play.