Patriots running back Rhamondre Stevenson wards off Sam Beal of the Giants to score his fifth touchdown of the preseason Sunday night in East Rutherford, N.J. Noah K. Murray/Associated Press

EAST RUTHERFORD, N.J. — Mac Jones is really pushing Cam Newton for the New England Patriots’ starting job at quarterback.

Jones, the first-round draft pick from Alabama, threw a touchdown pass and led three scoring drives as the Patriots capped a perfect preseason with a 22-20 victory over the winless New York Giants on Sunday night.

After the game, Patriots Coach Bill Belichick said a decision has not been made on a starting quarterback.

“We still have a lot of decisions to make,” he said.

This one certainly won’t be easy. Jones has gotten most of the preseason action and hit 36 of 52 passes for 388 yards and a touchdown. Newton, the starter last year in the post Tom Brady era, was 14 of 21 for 162 yards, a touchdown and an interception.

Jones said he would be ready to play, whether as the starter or backup.

“I’ve gotten a lot of opportunities to play and I can improve on everything I want to improve on,” Jones said after leading three scoring drives. “There’s a lot of work to do, but I think I’ve made progress.”

The Giants had a chance to tie the game in the waning seconds when backup Mike Glennon threw his second touchdown of the game, a 43-yarder to Damion Willis with eight seconds remaining. A potential tying 2-point pass play from Glennon to Dante Pettis fell incomplete. There is no overtime in preseason games.

Playing most of the second and third quarters, Jones finished 10 of 14 for 156 yards, including a go-ahead 17-yard TD pass to Isaiah Zuber early in the third quarter.

Newton started for the third straight game and again saw limited action, hitting 2 of 5 passes for 10 yards and throwing an interception. Nick Folk kicked a 41-yard field goal on the first series for the New England (3-0).

Rookie Rhamondre Stevenson scored on a 9-yard run in the third quarter and Quinn Nordin added field goals of 48 and 37 yards for New England, which missed the playoffs last year for the first time since 2008.

Belichick downplayed the perfect preseason.

“It’s important to win in the regular season,” he said.

The Giants, who lost all three preseason games, played their starters for the first time and the results were mixed. Daniel Jones finished 17 of 22 for 135 yards, including a 23-yard TD pass to tight end Kaden Smith just before halftime for a 7-6 lead. He also threw an interception on a play from the Patriots 1.

However, the starting offensive line failed to open lanes for the rushing game, allowed two sacks and a lot of pressures and hits.

Glennon threw a 12-yard TD pass to Alex Bachman in the third quarter.

NOT PLAYING

Because of injuries and rehabs, the Giants did not play wide receivers Kenny Golladay, Kadarius Toney, Josh Ross and Austin Mack, running back Saquon Barkley, guard Shane Lemieux, tight end Kyle Rudolph, defensive tackle Danny Shelton, cornerbacks Adoree Jackson and Josh Jackson, and linebacker Elerson Smith.

Golladay, Jackson and Rudolph were signed as free agents to bolster the offense and Toney was a first-round draft pick. Barkley is coming off knee surgery. The five did not play in the preseason.

DECISIONS

The Patriots will have to make a decision on a kicker between the 36-year-old Folk and the 23-year-old Nordin. Nordin has made 6 of 8 field goals in the preseason. This was Folk’s first game this preseason.

FASSEL TRIBUTE

Early in the second quarter, the Giants played a tribute to Jim Fassel, who coached the team from 1997-2003 and led them to a Super Bowl appearance February 2001. He died in June.

Some members of Fassel’s family were in the stands watching the game.

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