GLENDALE, Ariz. -- Even without their stars and other starters as well, the New England Patriots proved they are no pushovers when playing short-handed.

Just ask the Arizona Cardinals, who fell 23-21 Sunday night in the season opener for both teams at University of Phoenix Stadium.

"I'm happy to win, fortunate to win," Patriots coach Bill Belichick said. "We're going to need to play better next week and succeeding weeks."

It was good enough, though, to earn a road victory over a team that went 13-3 a year ago and advanced to the NFC Championship Game.

Playing without suspended quarterback Tom Brady, All-Pro tight end Rob Gronkowski, suspended defensive end Rob Ninkovich and two starting offensive linemen, the Patriots rode the arm of Jimmy Garoppolo and the leg of kicker Stephen Gostkowski to deal Arizona its first home loss in September since 2009.

The Cardinals rallied from a 10-0 first-quarter deficit and eventually took the lead with 9:46 left to play when Carson Palmer threw a 1-yard fade pass to Larry Fitzgerald in the corner of the end zone. Chandler Catanzaro's extra point made it 21-20, Arizona.

However, Garoppolo, charged with replacing Brady during the future Hall of Famer's four-game suspension for his alleged role in the Deflategate controversy, brought his team back and proved the Las Vegas oddsmakers, who listed New England as 9-point underdogs, to be dead wrong.

He guided the Patriots on a 13-play, 61-yard drive that was capped by Gostkowski's third field goal of the game, a 32-yarder, with 3:44 remaining. Gostkowski also connected from 47 and 53 yards.

"He's incredible," Patriots safety Devin McCourty said of Garoppolo. "All game he went out there and made the plays he was supposed to make. We knew as a team. We believed in him." There was no doubt in this locker room that Jimmy could go out there and play."

The Cardinals had a chance to win it, driving to the Patriots' 29-yard line in the final minute of play. However, Catanzaro was wide left on a 47-yard field-goal attempt. The snap from rookie Kameron Canaday was low to holder Drew Butler, which threw Catanzaro off.

"I wish I could take it back, but I can't," Canaday said. "I am just going to have to move forward and focus on next week and improving."

The Patriots took over with 41 seconds remaining and ran out the clock to seal the win.

"Obviously a very disappointing loss," Cardinals coach Bruce Arians said. "We really didn't play well enough in any phase -- from offense to defense to special teams -- to win this game, although we did have a chance to win at the end.

"We didn't execute our snap, hold and kick to win the game. That all starts with me, starts at the top. We were obviously not ready to play. They outplayed us, and we will learn from it and grow from it and continue. There's a long way to go and regroup and see if can win the next one."

Garoppolo finished the game 24 of 33 for 264 yards with one touchdown and no interceptions.

Palmer was 24 of 37 for 271 yards and two touchdowns, both of them to Fitzgerald, who moved into a tie for eighth all time with Hall of Famers Tim Brown and Steve Largent with 100 career touchdowns.

"Any time you lose a game, it's a tough pill to swallow," Palmer said. "But we'll bounce back. We need to bounce back. Anytime you lose the opener at home, it hurts. But there is too much football ahead of us. There are too many guys that love the game, have passion for the game and want to win and want to get it right."

The Cardinals converted a fumble by LeGarrette Blount into a touchdown in the third quarter. Second-year running back David Johnson bulldozed his way in for the score from a yard out. The touchdown by Johnson, who would finish with 89 yards on 16 carries and four receptions for 43 yards, pulled the Cardinals within 17-14.

Blount finished with 70 yards on 22 carries.

Chandler Jones had one of Arizona's two sacks against his former team, which traded him to the Cardinals last spring in exchange for guard Jonathan Cooper, who did not play because of a foot injury, and a second-round draft pick.

Garoppolo looked a little nervous on his first pass attempt of the night, sailing one over the head of Chris Hogan on New England's first possession. Garoppolo settled down almost immediately, though, completing each of his next four passes for 75 yards, which included a 37-yarder to Hogan down the left sideline for a touchdown.

Hogan beat the Cardinals' rookie cornerback, Brandon Williams, badly on the play.

After going 74 yards on eight plays, the Patriots mounted another scoring drive on their second possession, this time relying on the running game and the dual threat of Blount and James White to generate yardage. A great effort on third down by safety Tyvon Branch to deflect a Garoppolo pass prevented a touchdown.

New England went 63 yards on 12 plays but was forced to settle for a 47-yard field goal by Gostkowski.

The Cardinals pulled within three after forcing a New England turnover. Markus Golden strip-sacked Garoppolo and Jones, the former Patriot, recovered the fumble. Eleven plays later, Palmer hit Fitzgerald on a 3-yard scoring pass, and Arizona trailed just 10-7.

The touchdown moved Fitzgerald ahead of Torry Holt (13,382) for 14th on the league's all-time receiving yards list. Fitzgerald finished the game with eight catches for 82 yards.

The game marked the return of Cardinals Pro Bowl safety Tyrann Mathieu, who tore his right ACL last December. Mathieu didn't roam all over the field in typical Honey Badger fashion, though. He was used in a more conventional way as a deep safety.

The Cardinals lost two players to injury during the first half, as starting right guard Evan Mathis exited with a left foot issue and receiver J.J. Nelson departed with an injured left shoulder. Arizona has plenty of depth at the wide receiver position, but Mathis is a two-time Pro Bowl performer at guard. Earl Watford, a backup at all five positions up front, replaced him.

NOTES: Cardinals rookie CB Brandon Williams, when asked if he ever dreamed of starting in the NFL in Week 1 just a year removed from being a running back: "Of course, why wouldn't I? If you don't, there's something wrong. Everybody should have a dream like that." Williams finished with two tackles. ... Patriots WR Danny Amendola helped hold the American flag during the singing of the national anthem.