After forcing a Montana State punt, SMU (1-1) took over with 3:46 remaining on its own 19. Led by Gilbert, who finished 35 of 48 passing with 317 yards, the Mustangs took 14 plays to drive the remaining 81 yards for the win.
Joseph caught three passes on the game-winning march, finishing with 12 grabs for 113 yards.
Montana State raced out to a 22-5 lead before taking a 22-19 advantage into halftime. Cody Kirk and the Bobcats offense ate up the clock in the second half and, for the most part, kept the pass-happy SMU offense off the field.
Kirk finished with 107 yards and two touchdowns; including a 13-yard run that gave Montana State a 30-19 lead with 9:28 left in the third quarter.
SMU scored just one offensive touchdown before the game-winning drive, as the Mustangs settled for three field goals and turned the ball over twice inside the red zone. The Mustangs notched a safety in the first quarter to open the scoring, but it was their only lead until the final 12 seconds.
Montana State (1-1) was looking to become the ninth FCS team to beat a FBS team this season.
SMU, on the other hand, was licking its wounds after a 41-23 loss to Texas Tech, entering its most winnable non-conference game of the season.
The Mustangs, playing in the newly formed American Athletic Conference, have non-conference games at No. 7 Texas A&M and No. 24 TCU.
The top-two FCS teams, North Dakota State and Eastern Washington, both won games against the top tier of college football last weekend. Early on, Montana State looked like it would join them.
The Mustangs were trying to avoid their first 0-2 start since 1996 and first loss to a lower-tiered opponent since 1990. North Texas, which was Division I-AA at the time, topped the Ponies 14-7.
SMU was hampered by penalties (11 for 85 yards) and the inability to move the ball in large chunks until the waning stages of the game.
However, the Ponies' special teams came up with a big score just before halftime to put SMU back in the game.
JaBryce Taylor returned a punt 55 yards for a touchdown as time expired in the first half to give SMU the momentum heading into halftime, but behind Kirk's steady running, Montana State retook a double-digit lead on its opening drive of the second half.
The Bobcats built a three-score lead early by controlling the line of scrimmage on offense and preventing the Mustangs from stretching the field on defense.
While Gilbert was 17 of 26 in the first half, he only had 113 yards passing with a long of 18.
One of Gilbert's best plays of the opening 30 minutes was a pooch punt on fourth and 10 near midfield, which downed Montana State at its own 1. On the next snap, Cody Kirk was tackled in the end zone by Stephon Sanders to give the Mustangs a brief, 2-0 lead, before Kirk put Montana State up 8-2 with 2:23 remaining in the first quarter.
The Bobcats converted a pair of 2-point conversions in the swinging-gate formation.
Montana State quarterback DeNarius McGhee, who grew up less than 25 minutes from Gerald J. Ford Stadium in nearby Euless, finished 17 for 27 passing with 218 yards and a touchdown.
Florida State coach Jimbo Fisher hopes quarterback Sean Maguire is ready to go full speed by the middle of June.
Graduate transfer quarterback Davis Webb has officially joined California, giving the Golden Bears an experienced option to replace No. 1 overall NFL draft pick Jared Goff.
First-year football coach Dino Babers, hired by former Syracuse AD Mark Coyle, is on the committee that will search for Coyle's replacement.
Hugh Freeze has some major holes to fill on offense with the departures of Laremy Tunsil and Laquon Treadwell, but there is Chady Kelly and good depth.
After transferring in from Montana State, Dakota Prukop has a checklist he's working from as he prepares to compete for the Oregon job.
The destination for Week 6 of the Big 12 Ultimate Road Trip is unanimous, as all three conference reporters would head to the Red River Rivalry.