Sneed, a senior, completed 26 of 41 passes while leading the Grizzlies (5-1, 2-0 Big Sky Conference) back from a 17-0 deficit. He was also his team's leading rusher, piling up 67 yards and two touchdowns on the ground.
Sneed finished with a career-best 464 yards of total offense as the upset-minded Bengals (2-3, 1-1) fell off the pace after forcing three first-quarter punts.
"I'll say this about Dalton, his stat line is pretty fantastic, and his play in practice this week was pretty fantastic as well," Montana coach Bobby Hauck said. "But he's such a competitive guy he was awfully juiced up, and we missed some things in the first quarter. And after that he was money. It was just a great game by him."
Idaho State surged out of the gates, capping a 98-yard opening drive with a Ty Flanagan 1-yard run at 9:36 of the first quarter. Early in the second quarter Flanagan tore off a 71-yard scoring run to put the Bengals ahead 17-0.
Flanagan had 130 rushing yards on 18 carries.
Sneed then led touchdown drives of 68, 76 and 47 yards in the second quarter, all of them capped by Marcus Knight scoring runs of 4, 2 and 2 yards. Montana, ranked No. 8 in the STATS FCS Top 25, led 24-17 at halftime of its 100th Homecoming game.
Toure had eight catches for a career-best 188 yards, and Akem caught 10 passes for 135.
Sneed added two short scoring runs in the fourth quarter, hurdling a defender on the second one, that put Montana up 52-20 with 7:42 left in the game.
Both touchdown runs were set up by receptions covering 44 and 37 yards from Toure.
"He's a terrific receiver and has a lot of speed and I trust him to get behind the defensive back," Sneed said. "And that's what he did. He made phenomenal plays on two deep balls, keeping his feet inbounds. That's just him doing his thing."
Idaho State quarterback Matt Struck cooled off after 130 passing yards in that first quarter.
"We started having penalties and incomplete passes," Idaho State coach Rob Phenicie said. "You need to complete passes to continue to move the ball. The Grizzlies scored 24 points in the second quarter and I would bet there was a personal foul on each of those drives."
The Bengals were penalized 11 times for 121 yards. Struck, meanwhile, finished 16-of-33 passing for 189 yards. Michael Dean had six catches for 109 yards for Idaho State.
Montana got a final touchdown on a 51-yard run from Adam Eastwood with 5:27 left.
"Idaho State's got a good football team," said Hauck, who in his previous coaching stint at Montana had Phenicie as his offensive coordinator. "They came in and punched us and had us down big early on. I'm proud of our guys for our resilience and ability to fix things when they aren't going well."
Idaho State: The big-play Bengals took a 17-0 lead before surrendering it in the second quarter and then falling way off the pace after halftime. Struck passed for 189 yards, but just 41 in the second half.
Montana: A slow start was offset when quarterback Dalton Sneed caught fire and piled up a career-best 467 all-purpose yards. The Grizzlies amassed 31 first downs over the final three quarters.
Idaho State: The Bengals return home Saturday for a nonconference game against former Big Sky foe North Dakota.
Montana: The Grizzlies have a bye this coming Saturday and then travel to play Big Sky rival Sacramento State Oct. 19.
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