Brady completed 28 of 40 passes for 279 yards and did not have a turnover in the 25-23 win at MetLife Stadium in East Rutherford, N.J.
"We obviously didn't play the way we're capable of, but it's still good to go get a win," Brady told reporters. "[We are] 6-2 and obviously we've got a big [game] coming up this week."
Giants quarterback Daniel Jones led his team on a 13-play, 75-yard touchdown drive at the end of the game, connecting with Golden Tate on a 19-yard score before lining up for a two-point attempt to tie the score with 33 seconds remaining.
Jones threw a pass to his right, but Buccaneers cornerback Antoine Winfield Jr. swatted the pass away from Giants running back Dion Lewis to preserve the Tampa Bay lead. The Buccaneers then recovered a Giants onside kick to secure the victory.
"I'm proud of the way our players played," Giants coach Joe Judge said. "I've seen a lot of improved football, seen a lot of fight from our guys throughout the season.
"I continuously see an improved team on the field at all positions and guys playing for each other for 60 minutes. ... We're not asking for moral victories, we understand the people of New York deserve better, so we have to keep working to be better for them."
Ryan Succop made a 37-yard field goal for the Buccaneers on the game's opening possession and running back Ronald Jones fumbled on Tampa Bay's second drive. The Giants took advantage of good field position and scored after three plays on a Jones pass to Lewis.
The Giants pushed their advantage to 14-3 when Wayne Gallman ran for a two-yard score with 1:50 remaining in the second quarter. Succop then made another field goal just before the half to cut the Giants lead to 14-6 at the break.
Succop made his third field goal of the game on the Bucs' first possession of the second half. Tampa then forced a Giants punt before Brady orchestrated a five-play, 53-yard touchdown drive.
The veteran quarterback threw a three-yard touchdown toss to tight end Rob Gronkowski to cap off the possession and give the Buccaneers a 15-14 edge.
Graham Gano made a 33-yard field goal for the Giants on the next drive to give New York a 17-15 advantage.
Buccaneers cornerback Sean Murphy-Bunting intercepted Jones three minutes into the fourth quarter, setting up Brady for a six-play, 67-yard drive that ended with an eight-yard touchdown throw to Mike Evans. The touchdown gave the Bucs a 22-17 lead.
Succop added another field goal with 3:33 remaining before Jones led the Giants on their final touchdown drive.
The Giants quarterback completed 25 of 41 passes for 256 yards, two scores and two interceptions in the loss.
"It means a lot," Evans said. "In the past we would've found a way to lose a game like that. The defense made a play when it counted [and the] offense picked it up in the second half and found a way to win."
The Buccaneers (6-2) next host the New Orleans Saints at 8:20 p.m. EST on Sunday and the Giants (1-7) travel to face the Washington Football Team at 1 p.m. EST in Landover, Md.