TAMPA, Fla. -- Rookie quarterback Daniel Jones had an impressive first start in place of Eli Manning, rallying the New York Giants from an 18-point first-half deficit to a 32-31 victory over the Tampa Bay Buccaneers on Sunday.

Jones accounted for four touchdowns, including a seven-yard run on fourth down that put the Giants ahead for the first time with 1:16 remaining in the game.

"We had a chance there at the end of the game. That's all you can ask for," said Jones about the eight-play, 75-yard game-winning drive. New York's previous four possessions resulted in three punts and a turnover. "We kinda struggled to move the ball there at points and -- just a great job, great job moving the ball down the field as a team. We got some guys open, and they made plays. So great job, loved the fight and loved the grit of this win."

Jones finished 23-of-36 for 336 yards with two passing and two rushing touchdowns, flashing the poise and playmaking ability that made the Giants fall in love enough to make him the No. 6 overall pick in this year's draft.

Giants co-owner Steve Tisch told ESPN this was the beginning of a "new chapter." He was immensely impressed by the poise and composure of his 22-year-old quarterback. So too were his teammates. They raved about Jones afterward for the way he handled the huddle and seemed to fit in seamlessly in his first NFL start. There was even a moment in the second quarter with the Giants trailing 12-3 where Jones -- who rarely curses -- stepped into the huddle and yelled, "Let's f------ score!" according to wide receiver Russell Shepard.

Moments later, Jones kept the ball on a zone-read play for the go-ahead score.

The Giants (1-2) topped 17 points for the first time this season against a Todd Bowles-led defense that had looked solid the first two weeks. They escaped with the victory after Tampa Bay missed a 34-yard field goal attempt as time expired.

It was the Giants' first victory first victory when trailing by 18+ points at the half since 1949, according to Elias. They had lost 55 straight. Jones also became the second player since the 1970 merger to record two rushing TDs and two passing TDs in his first NFL start. The other was Detroit's Eric Hipple in 1981.

Manning had been the team's full-time starter for all but one game since 2004, but coach Pat Shurmur made the switch after last week's loss to the Buffalo Bills, saying that Jones was the better option for the Giants. The rookie proved Shurmur correct, at least in his first career start.

Jones led the Giants on four touchdown drives and flashed playmaking ability throughout. He ran for a touchdown in the first and second halves and used his legs on numerous occasions to create positive gains on plays that would have otherwise been dead.

"You can start to see -- and as you get to appreciate him as a player -- there's plenty of things he needs to do better. But as you get to -- there's certain things that I knew about this kid when we drafted him: He was tough, he was competitive, and in my opinion he's a winner," Shurmur said. "Now, the rest of it is just pure quarterback stuff. And because of those first three things, that's why he's gonna have a chance moving forward."

Jones rallied the Giants from a 28-10 halftime deficit. He hit tight end Evan Engram in stride running across the field for a 75-yard touchdown on the opening possession of the second half. He made a brilliant throw across his body deep downfield to fellow rookie Darius Slayton after shuffling around the pocket later in the third quarter. Later in that same drive, Jones dropped a perfectly placed ball into the arms of Sterling Shepard in the corner of the end zone for a touchdown, cutting the lead to 28-25.

What Jones showed on the field in his first career start was much the same as what the team has seen ever since he stepped into the building earlier this year. He checked all the boxes this spring and summer, and completed better than 85 percent of his passes during the preseason.

The lone knock was ball security. After three fumbles in the preseason, Jones lost a fumble on one of his four snaps late in the season-opening loss to the Dallas Cowboys. He also lost a pair of fumbles on Sunday when he was sacked in the third and fourth quarters against the Bucs.

But the positives significantly outweighed the negatives in this outing. Jones displayed impressive composure and poise not usually seen from rookie quarterbacks. It looked like he belonged right from the start when he completed five of his first six passes in the first quarter.

Jones' first career touchdown came on a 7-yard scamper early in the second quarter. It was a zone-read on which he kept the ball and outraced the nearest defender to the pylon. Bucs coach Bruce Arians noted in the week leading up to the game that the biggest difference between Manning and Jones was the youngster's mobility.

Jones finished with 28 yards on four rushes, but it was his ability to escape pressure on multiple plays that proved invaluable. As one coach told ESPN recently about Manning, when a play with him at the helm was off schedule, it "was over."

That clearly was not the case with Jones, as the Giants' offense scored more points Sunday than it had in the first two games combined. Not that the unassuming Jones was ready to proclaim his greatness after one start. He was asked after the game to give a postgame speech.

"No speech," Jones said. "Giants on three."