The victory is the fourth in a row for New York (5-2), which moved into sole possession of first place in the NFC East. Dallas, meanwhile, was looking to turn its season around, but lost quarterback Tony Romo to a broken left collarbone in the second quarter and fell to 1-5.
Hakeem Nicks, battling a hamstring strain, caught nine passes for 108 yards and two touchdowns. Steve Smith finished with nine receptions for 101 yards and a TD for the Giants, who scored 31 consecutive points to take control.
Romo was 5-of-7 for 39 yards and a touchdown before suffering his injury. Jon Kitna, playing for the first time since 2008, completed 16-of-33 passes for 187 yards and two touchdowns to Dez Bryant, who also returned a punt 93 yards for a score.
Bryant's second touchdown reception had Dallas within six points with 40 seconds to play, but the Giants recovered the onside kick and ran the clock out to seal the win.
"We seemed to have a big letdown when Tony went out," said Cowboys head coach Wade Phillips. "For whatever reason, our whole team let down a whole lot. I did think they kept fighting."
Manning's interceptions led to an early Dallas advantage. On the third play from scrimmage, Smith wasn't able to hang on to a high throw and he tipped it to Terence Newman, who returned the ball 30 yards to the Giants' five. Two plays later, Romo found Jason Witten for a four-yard score.
Three plays into New York's next drive, Nicks tipped the ball over the middle and it went to safety Gerald Sensabaugh. That put Dallas at the New York 18, and the Cowboys had a chance to get into the end zone again. But Miles Austin dropped the ball on 3rd-and-goal, and David Buehler kicked a 26-yard field goal.
The Giants rebounded with an 11-play, 79-yard drive that included some controversy. The Cowboys challenged a two-yard catch by Mario Manningham that moved the chains on third down, as Manningham reached the marker before moving backward and getting tackled. However, he was credited with forward progress and the call was upheld.
Several plays later, a Nicks reception was initially ruled incomplete before Giants head coach Tom Coughlin successfully challenged the call to keep the drive moving. Nicks also had a 24-yard catch-and-run to get the ball to the Dallas nine, then caught a seven-yard pass in the front of the end zone to get the Giants on the board with 2:58 left in the quarter.
Coughlin successfully used his second challenge on the final play of the frame, nullifying a punt downed at the one to set New York up at the 20 -- Dallas' Danny McCray was the first to touch the ball after it fell out of bounds. That possession ended in a Brandon Jacobs fumble, setting Dallas up at the visitors' 43.
On the first play, Giants linebacker Michael Boley drove Romo into the ground after the quarterback had released a pass. Romo landed on his left shoulder and exited the game. Kitna entered to help Dallas advance to the 23 before Buehler kicked a 41-yarder.
The Cowboys assumed a 20-7 advantage on Bryant's return. Matt Dodge's booming punt went 69 yards before Bryant picked up some blocks and raced into the end zone with 8:53 left in the half.
That's when New York started its comeback. The Giants' ensuing drive was highlighted by a 32-yard reception by Smith, who managed to bring in the ball despite being surrounded by defenders. Nicks capped the drive with an eight- yard score, again near the goal line, with 4:22 remaining.
After Dallas went three-and-out, New York took over at its 44 and needed just five plays to score again. Smith got separation from his defender and made the 14-yard catch as he fell in the back of the end zone, giving the Giants a 21-20 lead.
New York got another shot after recovering a fumble near midfield inside the final minute, and Lawrence Tynes kicked a 53-yarder through the uprights with two seconds left -- only after his initial 43-yarder was nullified by a holding penalty.
"In the second quarter we played outstanding," Manning said. "Flawless. Started moving the ball up and down. With three turnovers in the first half, to go into the game at halftime up four points, really all the momentum on our side, was big."
The Cowboys went three-and-out to start the second half, and the Giants once more started a drive in favorable field position, at their 45. The score came on a reception by Manningham, who used a block from tight end Kevin Boss to get to the right sideline. He raced toward the end zone, then sliced left between two defenders to give Big Blue an 11-point edge.
Jacobs then broke several tackles on a 30-yard touchdown run on the Giants' next possession, giving New York a 38-20 lead with 5:25 left in the quarter.
The Kitna-led Cowboys didn't have much offensive success until the middle of the fourth, when they reached the New York six on a 1st-and-goal. But Dallas turned the ball over on four consecutive incompletions.
After Ahmad Bradshaw fumbled for New York, Kitna fumbled, and Manning threw his third interception of the game, giving Dallas the ball at the New York 15 with 3:22 to play.
Kitna found Bryant for a score on the first play, and the two-point conversion to Roy Williams was successful. Buehler then waited for his onside kick to travel 10 yards before grabbing the ball, but it fell a yard short and New York gained possession. The Giants managed to drain 82 seconds off the clock before Tynes kicked a 26-yarder for a 41-28 lead.
Buehler's second onside kick caromed off a New York player, but the Giants' Clint Sintim quickly hopped on the loose ball to secure the outcome.
New York totaled a season-high 497 yards of offense, compared to 254 for Dallas...Bradshaw finished with 126 yards on 24 carries...Felix Jones had a team-high 35 rushing yards for Dallas. Witten ended with nine catches for 95 yards...Newman left the game for a brief time in the first period to get X- rays done on his ribs, which were apparently injured on his interception return...Bryant recorded the third-longest punt return in Cowboys history.