No. 2 Villanova (14-1) won the title in its first championship game appearance and 25 seasons after coach Andy Talley was hired to rebuild the program after the school's four-year absence from the sport.
"Our guys played great. Montana is a super team," Talley said.
Top-seeded Montana (14-1) was making a record 17th consecutive appearance in the playoffs. The Grizzlies, the 1995 and 2001 champions, lost to Richmond last year in the title game. Montana also lost in the final in 1996, 2000 and 2004.
Chris Whitney led an 81-yard drive, running for 22 yards on one play and connecting with Szczur for 26 yards on another. Whitney hit Chris Farmer with a 3-yard TD pass to give Villanova 16-14 lead with 5:26 left in the third quarter.
Whitney finished 10 for 13 for 142 yards, an interception and the touchdown. He also ran for 102 yards.
Montana's Andrew Selle threw a 53-yard touchdown pass to Jabin Sambrano to pull the Grizzlies to 23-21 with 1:07 left, but the onside kick attempt went out of bounds, and Villanova made a first down before running out the clock.
The Wildcats were down 14-9 at halftime after allowing the Grizzlies 246 yards passing in the first two quarters. Talley made adjustments, and the Wildcats found their pass rush after taking the lead.
Selle finished 12 for 35 for 351 yards and three touchdowns. Marc Mariani had 178 yards on nine catches before halftime, but didn't catch a single pass in the second half.
"We played really well in the second half and turned the tide," Talley said. "In the locker room our guys were pretty subdued, but we knew what we had to do."
Marquis Kirkland sacked Selle for a loss of 7 yards, ending Montana's last drive of the third quarter. The Grizzlies' next drive ended when Villanova's Eric Loper hit Sambrano so hard on third-and-12 he dropped a first-down catch.
Villanova wouldn't be denied. On fourth-and-1 at the Montana 3, the Wildcats went for it and Szczur plowed ahead into the end zone for the 23-14 lead with 11:04 left in the fourth quarter.
Montana had a shot at a 31-yard field goal on its first drive of the game, but Jeff Larson botched the hold and his pass attempt fell short.