FOXBOROUGH, Mass. -- It was not very pretty, but the New England Patriots will take it.

"It's tough to get a win in the NFL. Everything's tough. Every opponent's tough," tight end Rob Gronkowski said after scoring his team's only touchdown in a 21-13 victory over the mistake-prone Los Angeles Chargers on Sunday.

"Whenever we get a win, I'll take it -- no matter what. But definitely we gotta clean it up."

He was talking about the offense, which settled for six field-goal attempts by Stephen Gostkowski, who made four and missed a pair of 43-yarders as New England won its fourth straight heading into its bye week.

"I'm glad we won, that's the most important thing," said Tom Brady, who passed for 333 yards and raised his record to 7-0 in head-to-head meetings with Philip Rivers.

"Starting 0-1 and then being 6-2, a lot of mental toughness. That's good. We gotta keep it going. Our biggest games are ahead of us so we have to go play well."

The Patriots follow the bye with five road games, including one in Mexico City, in the next six games.

The four straight wins have come with New England scoring just 21.8 points per game.

"We didn't finish them off," Brady said of the drives. "I think we just have to do a better job of that. I know I've said that about 100 times this year, but it's tough. I mean, we're trying. It's just the execution is coming up a little short in critical times."

"Giving up too many big plays on defense and not converting on third down in the red zone -- two big issues," said Patriots head coach Bill Belichick.

The first of those issues, the 32nd play of 20 or more yards against the Patriots' defense, took place Sunday, with Melvin Gordon tying a 56-year-old club record with an 87-yard touchdown run -- the longest ever against Belichick's Patriots.

Brady, who threw a 2-yard touchdown pass to Gronkowski, recorded his 81st career 300-yard game and his fifth this season, which matches his total of last year.

The loss ended a three-game winning streak for the Chargers (3-5).

"This is a game we wanted, but we just have to go home and regroup and worry about next week," said Chargers safety Adrian Phillips. "We can't do anything about it now."

The worst of the many Los Angeles mistakes came when punt returner Travis Benjamin fielded a Ryan Allen punt near the sideline at his own 8. He ran backward and wound up fumbling the ball at the goal line, recovering it in the end zone for the first safety on a punt return in the NFL since 2003. That turned a 7-7 tie into a 9-7 New England lead, and the Patriots then marched to a field goal after the ensuing free kick.

Brady was 32-of-47 passing with 14 of the completions going to running backs. Rex Burkhead caught seven passes for 68 yards and James White had five for 85 yards.

Rivers hit Benjamin with a 24-yard touchdown pass in the fourth quarter.

After Gostkowski's final field goal, the Chargers had a chance in the final 62 seconds. They marched from their own 21 and got as far as the New England 24. As time was running out, Rivers, who threw an incompletion on a 2-point conversion after the Benjamin score, spiked the ball with one second remaining. But his pass on the next play was intercepted by Jonathan Jones at the 1 and the game was over.

"We had to defend the goal line," said Jones. "It was one of those things where we knew we didn't want to give up a score. We were able to come away with the play and seal the game."

Rivers finished 17 of 30 for 212 yards, a touchdown and an interception, while Gordon ran for 132 yards and Benjamin caught five passes for 64 yards.

In addition to the safety, the Chargers were guilty of numerous other mistakes, including having two touchdowns called back. One occurred when wide receiver Ty Williams had stepped out of bounds before coming back in to catch the ball and the other on an offensive pass interference call on a pick play.

"You aren't going to win a game if you have penalties (10) and dropped balls," said running back/returner Austin Ekeler. "It's pretty hard to win in the NFL doing that. We'll definitely go back and look at it and make those corrections."

NOTES: Patriots T Marcus Cannon left with a right ankle injury, while WR Chris Hogan left late with a shoulder injury. ... New England CB Stephon Gilmore, who had returned to practice on a limited basis this past week, missed his third straight game with concussion and ankle issues. He and CB Eric Rowe were still out. ... Los Angeles T Joe Barksdale missed his second straight game with a foot injury, while RB Branden Oliver (hamstring) returned after missing two weeks. ... Paul Lowe had an 87-yard touchdown run for the Chargers in the AFL in 1961. ... The Chargers also have their bye next week.