EAST RUTHERFORD, N.J. — The sight of New York Giants fans streaming for the exits with 11:31 remaining in Sunday’s game was as good a sign as any that the New Orleans Saints received the message.

What transpired after that moment proved they may still have a way to go.

Days after owner Gayle Benson publicly criticized her team’s recent performance in the midst of a three-game losing streak, the Saints went on the road and survived a furious fourth quarter rally to beat the New York Giants 34-27. At one point, the Saints scored 34 unanswered points to take a 34-10 lead, then survived as the Giants scored the game’s final 17 points and threatened to score again on the final play.

To snap their skid, the Saints found answers that have eluded them in recent weeks. The run game finally found its footing, gashing the Giants for 176 yards on the ground. New Orleans took care of the football when on offense and the defense made New York pay for its mistakes by forcing four turnovers of its own. A special teams unit that has been performing poorly made huge contributions in the kicking game, return game and in coverage.

It did not always look like the Saints were in line for such a rebound.

The Saints’ first five drives netted just 55 yards of offense. Quarterback Tyler Shough was erratic, completing just seven of his first 18 passes. Penalties torpedoed one drive when backup left tackle Asim Richards was penalized for holding on consecutive plays. Kicker Daniel Carlson missed a 55-yard field goal at the end of the Saints’ most promising drive.

Even when the Saints finally got on the scoreboard, it felt like a missed opportunity: Rookie Barion Brown returned a kick 41 yards to set up a short field near the end of the half, but Shough followed a clutch third and 6 throw with three straight incompletions that forced New Orleans to settle for a 58-yard Carlson field goal with 1:18 remaining in the first half.

The spark the team desperately needed came in the form of special teams ace Isaiah Stalbird on the ensuing kickoff, when he met Giants kick returner Charlie Jones like a heat-seeking missile.

Stalbird separated Jones from the ball, and rookie tight end Oscar Delp recovered the loose ball. It was as if a dam broke free after that play, with the New Orleans offense roaring to life to seize control of the game.

Shough ripped off a 25-yard run on the first play after the fumble recovery, setting New Orleans up at the goal line where he would eventually find Bryce Lance for a game-tying touchdown pass on fourth and goal.

That was the start of three consecutive touchdown drives for the Saints.

New Orleans then took the opening kick of the second half and put together its best drive of the game, culminating in a vintage Alvin Kamara touchdown reception in which he caught the ball near the right sideline and made three defenders miss on his way to a 31-yard score.

The defense forced a three and out on the ensuing possession, and Brown chipped in again by returning a punt 23 yards to set up another short field. Shough capped that drive off with a 1-yard plunge touchdown on third and goal.

Leading 34-10, New Orleans pulled its starters, but had to put them back in the game when New York refused to go away.

Giants starter Jameis Winston threw a pair of interceptions and took four sacks. New York pulled him from the game in the fourth quarter in favor of McCarthy, the former first round pick whom they acquired in a trade earlier this season.

McCarthy connected on several explosive passes against the Saints defense, including gains of 49 to Jones and 46 to former LSU star Malik Nabers. Running back Tyrone Tracy started the comeback with a 5-yard touchdown run on third and 2, and McCarthy closed the gap further with a 24-yard touchdown pass to tight end Isaiah Likely.

New York had an opportunity to tie the game or take the lead when it forced the Saints to go three and out inside the game’s final two minutes. The Giants took over at their own 29 yard line with 57 seconds remaining, trailing by seven and with no timeouts remaining.

McCarthy evaded pressure in the backfield on the first play of the drive, finding a wide open gap in the Saints defense for a 28-yard scramble, then he hit Likely for a gain of 23 on the next play to push the ball inside the Saints’ 25.

But the Giants rally fizzled when McCarthy’s fourth and 1 pass with 12 seconds remaining sailed high and out of bounds over Likely’s outstretched hands.