Luton completed all seven of his passes on the eight-play winning drive as the Beavers avoided a startling upset in the back-and-forth game against an FCS opponent.
Portland State's final possession ended with a missed 46-yard field goal by Grayson Kennedy that would have forced overtime.
Josh Kraght, who earlier caught a pair of touchdown passes, stepped in at emergency quarterback and leaped over the pile from a yard out to give Portland State a 32-26 lead with 2:43 left in the game. Kraght either ran or passed on eight of the nine plays in that drive, accounting for 56 of the 67 yards on the possession.
After falling behind 20-14 in the third quarter when Portland State used a pair of turnovers to set up touchdown drives, the Beavers struck back with two touchdowns in a span of 89 seconds to regain the lead.
The first came when backup running back Trevorris Johnson, a transfer from TCU, ran in from 3 yards out. That followed a kickoff return to midfield and a 48-yard pass from Luton to tight end Noah Togiai. Three plays after the Johnson touchdown, Oregon State linebacker Manase Hungalu returned an interception 21 yards for a score to put the Beavers up 28-20.
Portland State (0-2) pulled within 28-26 to end the third quarter on Jalani Eason's second touchdown pass to Kraght, this one covering 37 yards.
Oregon State (1-1) used two long drives, covering 81 and 98 yards, to build a 14-6 halftime lead.
Running back Ryan Nall scored the first touchdown for the Beavers on a 1-yard run after Portland State took a 6-0 lead on the game's opening drive. The Oregon State offense then stalled on three consecutive three-and-out possessions before marching from its own 2-yard line in eight plays, with backup quarterback Darell Garretson running 4 yards for the score.
The Vikings, who last week lost 20-6 at BYU, led 6-0 by going 79 yards on the game's first possession, capped by a 42-yard pass from Eason to Kraght.