TAMPA, Fla. — It is the dawn of a new day in Giants football — as wide open and inviting as the green grass in front of Daniel Jones as he ran to glory, sprinting into the end zone to stamp his arrival as official.

In an NFL starting debut for the ages, Jones was calm and cool, cajoling one moment, cursing up a storm the next, poised and passionate, wowing with his arm and legs. The Giants needed every bit of everything he could give.

“We’re all still trying to figure DJ out,’’ receiver Russell Shepard said. “He’s probably like the world’s most mysterious man.’’

The unwrapping of the mystery began Sunday, amid some terrible adversity around him. Jones faced an 18-point halftime deficit against the Buccaneers and was without the services of the Giants’ best player, Saquon Barkley, lost to a high ankle sprain.

The rookie quarterback, leading a furious comeback, needed 7 yards to show the difference, above all else, he brings to the field that separates him from franchise icon Eli Manning. Jones scored on a pressure-packed fourth-down scramble, a 7-yard touchdown run with 1:16 remaining to put the Giants ahead 32-31.

Moments later at Raymond James Stadium, the Giants secured their first victory of the season, but not before Janoris Jenkins gave up yet another huge play to Mike Evans and Matt Gay missed what would have been the game-killer for the Giants, going wide right on a 34-yard field attempt as time expired.

“The football gods were on our side,’’ receiver Sterling Shepard said.

Jones was 23-of-36 for 336 yards and two touchdown passes. He did not throw an interception, though he did lose two fumbles. He also ran for two touchdowns.

“He played phenomenal,’’ Sterling Shepard said.

As the Giants — victimized so often the past few years by late field goals that beat them — raced onto the field to celebrate, Manning found Jones and gave him a hug.

“He was just happy for me,’’ Jones said.

“Felt like we won the Super Bowl out there,’’ center Jon Halapio said.

This made the Giants 1-2 and in some ways it felt like a new beginning. But it came with a sobering price. Barkley, bottled up all game, came off the field after making a 6-yard reception in the second quarter and spent the second half on crutches, wearing a protective boot on his right foot.

He could be out for 6-8 weeks.

“I’ve never really been hurt before,’’ a downcast Barkley said. “Whatever it is, I promise you I’m coming back 10 times better.’’

The Giants trailed 28-10 at halftime, as their shabby defense allowed the Buccaneers to score on all six of their possessions, with Evans hauling in three touchdown passes.

“I’m so proud of the guys,’’ Sterling Shepard said. “We came in here, we saw Saquon on crutches and a lot of people would be defeated at that moment. But we didn’t bat an eye.’’

Teammates saw a new side of Jones. He got in the faces of his offensive linemen.

“Give me some time, give me some time, I’ll make something happen,’’ Halapio said, relaying Jones’ pleas.

Jones stunned his older teammates with his language.

“It was the F-word and I loved it,’’ Russell Shepard said. “There were some good ones.’’

The first time he touched the ball in the second half, Jones hit tight end Evan Engram on a catch-and-run that turned into a 75-yard touchdown. The comeback was on. Suddenly, the Giants, on defense, were forcing punts and allowing only three points in the second half.

Jones found rookie Darius Slayton for 46 yards and, with perhaps his best throw of the game, fired a laser to diving Sterling Shepard in the right corner of the end zone to make it 28-25.

“I think we showed a lot of fight and we battled back after creating a hole for ourselves,’’ Jones said.

The game-winning drive got going on a 21-yard pass to Slayton and then a 36-yarder to Sterling Shepard. From the 7-yard line, Jones had his targets

spread out and as soon as he got the snap he saw nothing in front of him, except a pathway to his first fourth-quarter comeback.

“It just opened up — I saw grass and took it,’’ said Jones, who sprinted into the end zone untouched.

“You guys see his wheels?’’ Sterling Shepard said. “It’s something serious.’’

It was, ironically, a play Manning, 38, does not make and does not even attempt.

“Eli was an athlete — he’s the best athlete out of the Mannings,’’ Russell Shepard said. “He’s just old as hell at times.’’

When Gay — who missed two extra points in the first half — misfired again, Jones and the Giants were winners.

“He’s mature beyond all our years,’’ coach Pat Shurmur said.

“We’re gonna ride with him until the wheels fall off,’’ Russell Shepard said of Jones. “We’re extremely excited in him and extremely confident what he can do for us as a team. We just love him.’’