Culpepper connected on 19 of 27 passes for 235 yards. Moss, returning after missing three games with an injury, caught four passes including the touchdown toss, which sent the Vikings ahead to stay in the third quarter.
Kevin Williams recovered a fumble and ran 77 yards for a Vikings touchdown late in the game.
Fred Taylor ran for 147 yards for the Jaguars and Brian Leftwich passed for 235 yards and a touchdown.
Minnesota is 7-4, Jacksonville 6-5.