Villanova led 20-7 at the half but had four punts in the second half before Randall Harris and Evan Horn ended the last two possessions with interceptions. Horn's second pick, inside the 10, came with 14 seconds left.
Brosmer completed 25 of 32 passes for 276 yards and one interception. He capped an 80-yard game-opening drive with a 15-yard strike to Brian Espanet. Villanova scored three touchdowns, with Daniel Smith running for one and passing for another, to build the halftime lead.
The first Brosmer-Laube scoring hookup, covering 21 yards, put New Hampshire up 21-20 with 5:34 to go in the fourth quarter. The second, for 21 yards, came with 8:49 to play.
New Hampshire (5-3, 4-1 Colonial Athletic Association), had 403 yards of total offense.
Villanova (6-3, 3-3) piled up 398 yards with Smith going 21 of 40 for 313.
Tight end Jahleel Billingsley transferring from Alabama Crimson Tide to Texas Longhorns
Jahleel Billingsley will reunite with Texas coach Steve Sarkisian, who was Alabama's offensive coordinator in 2020 when the tight end emerged as a playmaker.
Alabama Crimson Tide LB Drew Sanders transferring to Arkansas Razorbacks
Drew Sanders, who was ESPN's No. 36 overall player in the 2020 recruiting class but has played mostly special teams for Alabama, is transferring to Arkansas.
Kirk Ferentz disbands diversity group, says decision unrelated to leader's suggestion to move on from Iowa coach
Iowa coach Kirk Ferentz has disbanded an advisory committee that was created following evidence of racial bias in his football program, with a report saying the group's leader had suggested it was time for the school to cut ties with Ferentz.
NFL draft order for 2022: First-round picks from 1 to 32, including Jaguars, Lions and Texans in top three
Jacksonville will have back-to-back No. 1 overall picks, while Detroit and Houston follow at the top of Round 1.
Notre Dame hiring Al Washington as defensive run game coordinator and defensive line coach, sources say
Notre Dame is hiring Al Washington as its defensive run game coordinator and defensive line coach, sources said.
Louisville football hires Notre Dame assistant Lance Taylor to be new offensive coordinator
Notre Dame assistant Lance Taylor has been named the new offensive coordinator at Louisville.