Barton, in just its fourth season as a Division II program, avenged a 37-17 loss to the Wildcats last season.
Davidson (0-2), which lost to VMI 12-7 in a season opener, had a 13-game home winning streak snapped. The Wildcats had won their last seven home openers dating to 2016.
Barton scored 20 unanswered points in the second quarter to take a 27-21 at halftime. Lynch was 7-of-9 passing for 155 yards and a touchdown in the first half, and he also carried it six times for 48 yards and two scores.
Davidson scored the first 10 points of the second half to take a 31-27 lead on Adam Zouagui's 35-yard field goal. After both teams punted, Barton went on a 12-play, 83-yard drive, capped by Jordan Terrell's 13-yard touchdown run with 5:57 left.
Davidson had the ball at its 39 with 2:59 remaining in the fourth quarter, but Coulter Cleland's pass was intercepted by Kermit Solomon. Barton was able to run out the clock.
Terrell, who rushed for 186 yards last week, carried it 22 times for 140 yards and two scores for Barton.
Cleland was 10 of 20 for 142 yards with a touchdown and interception for Davidson. Mari Adams rushed for 115 yards and Sam Valor added 55 yards on the ground with a score.
The game was moved up one day due to a severe weather predicted for Saturday.
AP college football: https://apnews.com/hub/college-football and https://apnews.com/hub/ap-top-25-college-football-poll
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