FOXBOROUGH, Mass. — Aldrick Rosas hit a 48-yard field goal as time expired and the New York Giants earned a 40-38 win over the New England Patriots in the final exhibition game for both teams Thursday night.

The Giants scored 34 points in the first half, but the Patriots outscored them 24-3 over the final 29 minutes before Rosas’ field goal. It helped salvage a night in which Geno Smith and Josh Johnson each had touchdown passes, and the Giants’ defense returned an interception for a touchdown.

Third-stringer Jacoby Brissett threw for 341 yards and four touchdowns, and ran for another to nearly lead the Super Bowl champions back from a 20-point halftime deficit. Stephen Gostkowski hit a 55-yard go-ahead field goal with 44 seconds remaining.

As expected, both teams rested their key contributors in advance of Saturday’s reduction to a 53-man roster.

Smith entered the night with the inside track to win the Giants’ backup quarterback job behind Eli Manning. He took a big step toward locking it up, completing 10 of 11 passes for 111 yards and touchdown. Smith was signed to a one-year contract in March and was brought in to compete for the job behind Manning and has done well.

The Patriots open the regular-season at home next Thursday against Kansas City. The Giants open at Dallas on Sept. 10.

New York safety Darian Thompson was the only projected starter to see any action.

After some lackluster efforts, Johnson also had his best performance of the preseason. He completed 11 of 14 passes for 135 yards.

As strong as Brissett’s performance was, it still might have been his final game for New England. Brissett started a pair of games last season during Tom Brady’s four-game “Deflategate” suspension after backup Jimmy Garoppolo was injured. But it is unclear if the Patriots will keep a third quarterback with Brady available to start this season. So Thursday could have served as Brissett’s audition for his next NFL team.

Tight end Matt LaCosse entered Thursday on the bubble and helped himself with touchdown catches of 25 and 2 yards. His stock also got a boost thanks to a first-half fumble by fellow tight end Will Tye.

NOTES: The prospects for Patriots second-year DB Cyrus Jones surviving Saturday’s roster cut took a major hit early in the second quarter when he left with a right knee injury. New England selected Jones 60th overall in the 2016 draft. He got his feet tangled while defending a deep pass along the sideline to Travis Rudolph and tumbled to the turf. He needed the help of two trainers to get off the field. The Patriots originally had high hopes for Jones, a star at Alabama as a defensive back and kick returner. But he struggled throughout last season, with fumble issues on special teams. He was a healthy scratch for five of New England’s final six games, including the entire postseason run. Jones has shown improvement in ball security this preseason. But he’d also made mistakes in coverage that left him on the bubble to make the roster.

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