The Spartans survived four turnovers in the first meeting of ranked teams in the 2012 college football season, one of the miscues leading directly to Boise State's only touchdown.
The Broncos took a 13-10 lead with 4:23 to go in the first half on the second field goal of the game by Michael Frisina.
That remained the score until Andrew Maxwell led Michigan State on a 56-yard, 9-play drive that led to Bell's second touchdown of the contest.
Bell, who gained 210 yards on a massive 44 carries, produced a 1-yard touchdown midway through the first period.
Michigan State had a 10-3 lead midway through the second period when Jeremy Ioane intercepted a tipped Maxwell pass and returned it 43 yards for a touchdown.
Maxwell went 22-of-38 for 248 yards, but was intercepted three times.
Joe Southwich completed 15-of-31 passes for 169 yards and an interception.
After Bell's go-ahead touchdown, Boise State drove to the Michigan State 42 before running out of downs. Michigan State then ran off the game's final 6:26 with Bell carrying the ball nine times in 11 plays.