Tampa Bay was hampered by three missed field-goal attempts by kicker Nick Folk.
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.
Tampa Bay rallied within striking distance on Jameis Winston's red-hot fourth quarter, including an 18-yard touchdown pass to tight end Cameron Brate with 2:09 remaining.
The Bucs failed on their onside kick, and New England drove for a cushion score on Stephen Gostkowski's 48-yard field goal -- his fourth field goal of the game -- with 1:10 to play.
Tampa Bay had a final opportunity, driving to the Patriots 19-yard line with three seconds remaining before Winston threw an incompletion near the goal line on the game's final play.
Folk's struggles continued as he missed a 31-yard attempt with 5:36 remaining that would have trimmed the deficit to 16-10. He also failed to convert from 56 and 49 yards and has made only one field goal in his last six attempts.
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.
Winston completed 26 of 46 passes for 334 yards, but he went 14 of 21 for 225 yards in the fourth quarter.
New England committed 12 penalties for 108 yards, but the Bucs had the game's costliest penalty. 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.