But backup quarterback Daniel Raudabaugh rallied Miami to 17 points in the final 6:35 of regulation, throwing for 202 yards and two touchdowns and driving the RedHawks 61 yards in less than two minutes to set up Trevor Cook's game-tying field goal.
Andre Bratton's 4-yard run gave the RedHawks (1-1) the lead in the first overtime, but Weber came right back with a 25-yard TD pass to Eric Decker on third-and-10 to tie it.
Jason Giannini's third missed field goal of the game was a 26-yarder that went wide left in the second overtime, and Cook had a chance to win it for Miami.
But his 33-yarder was wide right.
Gophers cornerback Jamal Harris was victimized through the air all afternoon, and he dropped a sure interception on second down in the third overtime. But on third down, Raudabaugh was hit by Deon Hightower, and his pass fell right into the arms of Harris in the end zone.
Pinnix ripped off a 20-yard run, then scored from 2 yards out to allow the Gophers to escape what would have been their second straight overtime loss to an opponent from the Mid-American Conference.
Last week the Gophers rallied from a 21-0 halftime deficit to force overtime against Bowling Green, but lost when the Falcons went for two points on the last play of the game.
Raudabaugh threw for 222 yards, two TDs and an interception after starter Mike Kokal threw for 196 yards and a touchdown in the first three-and-a-half quarters.
Chris Givens had five catches for 112 yards for the RedHawks, who lost star linebacker Joey Hudson to a knee injury on the second series of the game. Hudson watched most of the game from the sidelines on crutches and will have an MRI on his left knee in the next few days, coach Shane Montgomery said.
Starting tailback Brandon Murphy rushed 12 times for 78 yards, but injured his knee in the fourth quarter and will also need an examination.
Weber threw for 271 yards and four touchdowns for Minnesota and rushed for 97 yards and another score in a huge step forward after his first career start against Bowling Green.
The Gophers rushed for 306 yards and Eric Decker had seven catches for 128 yards and two touchdowns, including a 59-yarder through two Miami defenders to open the fourth quarter.