TAMPA, Fla. — The first prominent high note in the Daniel Jones era of Giants football was a daring 7-yard touchdown scamper in the second quarter of Sunday’s game against the Tampa Bay Buccaneers. It was a play that symbolically breathed new life into the Giants, whose sideline was clearly buoyed not just by the score but by its execution.

Here was a bold, designed dash by a rookie quarterback with the kind of dexterous mobility so common to the cadre of young quarterbacks lighting up the N.F.L. in the last two seasons.

About two hours later, Jones stood in the pocket on a critical fourth-down play in the game’s final two minutes. Starting his first game as Eli Manning’s replacement, Jones had been banged around by the Buccaneers defense, sacked five times and fumbled twice. He was missing his best offensive weapon, All-Pro running back Saquon Barkley, who was in the bench area on crutches with a sprained right ankle. Jones, whose Giants trailed by 18 points at halftime, was in a visiting stadium, enveloped by a raucous crowd that was on its feet roaring for the home team to hold a late, six-point lead and thwart this new-to-the-N.F.L. quarterback.