Peterson ran 17 times for 84 yards and two touchdowns for the Vikings, who led for most of the second half until Blaine Gabbert's 39-yard touchdown heave with 20 seconds left in the fourth quarter put the Jaguars back in front.
For the first time since the NFL's new overtime scoring rule was installed last season, the first team on the board didn't immediately run off the field a winner.
After Walsh's 38-yard kick, the Vikings had to play defense again while the Jaguars had their chance to match. But Gabbert was hurried into a fourth-down overthrow, spoiling the debut for new Jaguars coach Mike Mularkey.
Lions 27, Rams 23
Stafford made up for a shaky game by leading an 80-yard, nine-play, game-winning possession that included three passes of at least 18 yards.
Sam Bradford directed a go-ahead drive that set up Greg Zuerlein's 46-yard field goal and put the Rams ahead 23-20 with 1:55 left. But coach Jeff Fisher's debut ended with a loss because the Rams could not shut down Stafford in the end.
Stafford had three interceptions before halftime for the first time in his four seasons. Cortland Finnegan had a 31-yard interception return for a TD that gave the Rams a 13-7 lead late in the first half.