EAST RUTHERFORD, N.J. -- Julio Jones finished with 13 receptions for 135 yards, including a 37-yarder that set up the game-winning touchdown run by Davonta Freeman to give the Atlanta Falcons a 24-20 win over the New York Giants at MetLife Stadium on Sunday.

Wide receiver Jones, last week's NFC Offensive Player of the Week, fought through a hamstring injury that kept him out of practice two days this week.

Jones, who connected with quarterback Matt Ryan for six receptions for 44 yards in the first quarter alone, recorded 25 of those first-quarter yards on the Falcons' second drive of the game. That drive culminated in a 7-0 lead on a 1-yard touchdown pass from Ryan to running back Tevin Coleman.

"Every opportunity that I get when a ball is thrown at me, I feel like it's my job to catch it," Jones said. "I had 15 targets today and I caught 13. I think I did OK today. I wish I could have caught all 15, but it happens."

Originally, the Giants had their starting cornerbacks, Prince Amukamara and Dominique Rodgers-Cromartie, switch sides in covering Jones.

However, Rodgers-Cromartie had to leave the game after the first play when he suffered a stinger.

Although Rodgers-Cromartie returned to the game, his return was short-lived as he was concussed.

Rodgers-Cromartie's exit from the game left Amukamara to cover Jones, who got the better of the veteran cornerback, including a one-handed 10-yard grab on a third-down conversion in the third quarter that helped keep a Falcons scoring drive alive.

"Julio is one of the best wide receivers in the game, and I feel like I'm starting to be one of the best in the game," Amukamara said. "It was good on good; he just made a play. It was a good throw and catch."

That good throw and catch ultimately led to the Falcons slicing the Giants' lead to 20-17 when Ryan connected with receiver Leonard Hankerson early in the fourth quarter for a 10-yard touchdown toss.

New York, who got on the board early in the second quarter on a 38-yard field goal by Josh Brown to make it 7-3, managed to clamp down on Jones in the second quarter, holding him to three receptions for 15 yards.

Giants receiver Odell Beckham Jr., who finished with 146 yards on seven receptions and one touchdown, then took his turn at center stage.

Beckham's 67-yard second-quarter touchdown reception, his 101st career reception, tied the game at 10 with 3:34 left in the second quarter.

With the Giants opening the second half with a 13-10 lead thanks to a 44-yard field goal by Brown, New York extended their lead by 10 points.

Running back Shane Vereen, who finished his big day with a team-leading eight receptions for 76 yards, caught a big 37-yard third-down conversion that set up a 1st-and-10 at the Falcons' 16-yard line.

Three plays later, Giants quarterback Eli Manning found tight end Larry Donnell in the end zone for a 10-yard score to make it 20-10.

After the Giants held the Falcons to a three-and-out on the ensuing possession, the momentum temporarily swung back to Atlanta's favor when defensive end Kroy Biermann sacked Manning for a three-yard loss late in the third quarter, stripping the ball loose.

"We're a ball attacking team, so we're going after the ball every play," Biermann said of the Falcons' big fumble recovery.

Linebacker Paul Soliai fell on the loose ball at his own 9-yard line for no gain, snuffing out the Giants' drive. That set the Falcons up for their 12-play, 91-yard drive ending with Hankerson's touchdown reception.

The Falcons snatched the victory on Freeman's 2-yard score with 1:58 left, a drive set up by a 37-yard reception by Jones.

"We work on that every day. It wasn't anything new to us," Jones said of the final drive. "No one got tight at any time in the game when we were down. We just went out there and made plays like we usually do."

The game could prove costly to the Giants (0-2), who won't have much time to dwell on this latest loss since they have a short week ahead thanks to a Thursday night home game against Washington.

NOTES: With the win, Atlanta takes the lead in the regular-season series, 12-11. ... Falcons QB Matt Ryan extended his NFL-record setting streak of throwing for at least 200 yards in road games to 33. ... Giants QB Eli Manning, who began the game needing 52 passing yards to reach 40,000 in his career, accomplished that feat in the second quarter. Manning becomes the 15th signal caller to hit the 40,000 mark in NFL history. ... Falcons WR Julio Jones' 13 receptions tied a franchise high set by tight end Tony Gonzalez on Oct. 7, 2012. ... The Giants celebrated the 25th anniversary of their Super Bowl XXV Championship team during halftime. ... The Falcons (2-0) will play their third consecutive NFC East opponent when they visit the Cowboys next weekend. They edged their two opponents, the Eagles and Giants, by two and four points, respectively.