TAMPA, Fla. -- The New England Patriots went from suffocating to exasperating but still achieved their goal.

They got a much-needed victory.

Utilizing dominance through three quarters, then hanging on by their fingernails in the fourth, the Patriots escaped with a 19-14 victory against the Tampa Bay Buccaneers on Thursday night at Raymond James Stadium.

"There are still a lot of things we need to work on," Patriots coach Bill Belichick said. "There are things we can do better, but I think our whole defense competed well."

New England (3-2), which allowed an NFL-high average of 456.8 yards in its first four games, stifled the Bucs (2-2) through three quarters.

However, Tampa Bay, which finished with 409 yards, put on a furious fourth-quarter rally. The Bucs got within striking distance on Jameis Winston's 18-yard touchdown pass to tight end Cameron Brate with 2:09 remaining, then had one final possession.

Winston, who was 13 of 21 for 225 yards in the fourth quarter alone, drove Tampa Bay to the New England 19-yard line with three seconds remaining.

His final-play pass near the end zone, intended for rookie tight end O.J. Howard, fell incomplete.

"The quarterback has to make a play in that situation," said Winston, who was 26 of 46 for 334 yards overall. "I didn't give my guys the opportunity to make a play."

The loss can hardly be pinned on Winston, though.

Bucs kicker Nick Folk missed three field-goal attempts, including a 31-yarder with 5:36 remaining that would have trimmed New England's lead to 16-10.

Meanwhile, Patriots kicker Stephen Gostkowski connected on four field-goal attempts, including a 48-yarder with 1:10 to play that provided a needed cushion.

Folk also failed to convert from 56 and 49 yards, and he has made only one field goal in his past six attempts.

Through three quarters, Winston had passed for just 109 yards. Tampa Bay failed on its first seven third-down conversions.

"Early on, we just couldn't get into a rhythm," Bucs coach Dirk Koetter said. "When we started playing helter-skelter, that's when we started to move it. That's the no-huddle theory. That's when we seemed to move it. We needed to do it much earlier than we did."

Patriots cornerback Stephon Gilmore said, "We gave up some yards, but I think we got better (than in previous games). (Winston) made some great throws. I've got to tip my hat to him. But we did some things to slow him down (earlier in the game). We got a win, and that was what we really needed."

Patriots quarterback Tom Brady completed 30 of 40 passes for 303 yards with one touchdown and one interception.

The Patriots also got field goals of 27, 23 and 45 yards from Gostkowski.

New England committed 12 penalties for 108 yards, but the Bucs had the game's costliest penalty in the fourth quarter. Trailing 16-7, with third-and-goal from the Patriots 3-yard line, Winston scored on a scramble, but the play was negated by an illegal-use-of-hands penalty on offensive lineman Evan Smith.

Winston threw an incompletion from the 13, and Tampa Bay opted for Folk, who was wide left on his 31-yard attempt.

Utilizing a pair of long scoring drives, New England led 13-7 at halftime.

The Patriots opened the scoring on Gostkowski's 27-yard field goal, capping a 13-play, 89-yard drive, which began at their 2-yard line after a 45-yard punt from the Bucs' Bryan Anger.

Tampa Bay took a 7-3 lead with 8:26 remaining in the half, getting a 1-yard touchdown run from Doug Martin, back in action after serving a four-game suspension for violating the NFL's substance-abuse policy.

The Patriots regained their advantage 10-7 on Brady's 5-yard pass to Chris Hogan that completed a nine-play, 75-yard march. Gostkowski tacked on a 23-yard field goal with 40 seconds remaining in the half.

NOTES: The Patriots were without inactive TE Rob Gronkowski (thigh), a late addition to New England's injury report on Wednesday. ... The Bucs played without three defensive starters -- LB Kwon Alexander, LB Lavonte David and S Keith Tandy -- who were inactive. Alexander missed his third consecutive game. ... Tampa Bay rookie S Justin Evans, making his first NFL start, intercepted a pass from QB Tom Brady on New England's opening drive. ... Malcolm Glazer, the former Bucs owner who died in 2014, was inducted into Tampa Bay's Ring of Honor at halftime. Glazer purchased the franchise in 1995 and presided over its best times -- five playoff berths in seven seasons and a championship in Super Bowl XXXVII. ... Brady won his 186th regular-season game, tying him with Peyton Manning and Brett Favre atop the all-time list. ... Brady made his 240th NFL start, tying former Miami Dolphins QB Dan Marino for third place on the all-time list. Favre (298) and Manning (265) are the top two.