GREEN BAY, Wis. -- Philip Rivers threw for 503 yards. He needed 3 more.

The San Diego quarterback's 65th and final pass, on fourth-and-goal from the 3-yard line, was batted down at the goal line by Green Bay cornerback Damarious Randall, giving the Packers a 27-20 victory over the Chargers at Lambeau Field on Sunday.

Rivers recorded just the 17th 500-yard game in NFL history, and he completed 43 of 65 passes for two touchdowns with no interceptions.

Packers quarterback Aaron Rodgers threw two touchdown passes, and running back James Starks rushed for 110 yards, including a 65-yard run that staked Green Bay to a 14-3 lead in the first quarter.

Chargers wide receiver Keenan Allen caught 14 passes for 157 yards, including an NFL season-high 11 in the first half, but he missed most of the second half with a hip injury.

The Packers took a 27-20 lead on kicker Mason Crosby's 28-yard field goal with 2:37 remaining.

Rivers drove the Chargers the length of the field, leaning heavily on tight end Antonio Gates and running back Danny Woodhead. On fourth-and-goal with 20 seconds remaining, Rivers went to Woodhead to his right in the flat, but Randall closed and broke it up to save the game.

"They actually ran that play earlier," Randall said. "Rivers was trying to see if he could get it to Gates first. I guess No. 39, Woodhead, was his second option, and I was just there to make a play."

The Packers are 6-0 for the first time since 2011 and the second time in the last 50 years. For the first time in a long time, it is the defense -- not the Rodgers-fueled offense -- making the key plays.

Still, the Chargers made Green Bay sweat.

"If you have a chance to study their offense, (Rivers) is so accurate with the football and the at-the-line offense and the command of recognizing the defense and so forth, you've got to give him a ton of credit there," Packers coach Mike McCarthy said. "It was a competitive match, but we kept them out of the end zone. That's what was most important. When you get in games like that, where you're giving up a lot of yards, at the end of day, it's about field goals versus touchdowns, and that was obviously a big part of this game."

The Chargers (2-4) have lost games in the final moments in back-to-back weeks, and three of their losses were by no more than seven points.

"Gosh, I don't know, you have to laugh to keep from crying," said Rivers, who set team single-game records for completions, attempts and yards. "Another one. Another one that was tough. And as good as we played, in a lot of ways, we left plays out there that we normally make. ...

"We should've scored 40. We should've. And that's what's frustrating because our defense played their tail off."

San Diego, which fell behind 17-3 in the first half, trailed 24-20 when it got the ball at its 29 with nine minutes remaining in regulation. On the first play, Rivers threw a short pass to Gates that the tight end turned into a 21-yard gain. Another short pass turned into a gain of 14 by running back Branden Oliver, but the Packers' defense -- run ragged for most of the final three quarters -- stiffened with a third-down sack.

Following a Chargers punt, Rodgers hit tight end Richard Rodgers for 25 on a naked bootleg, then avoided unblocked cornerback Patrick Robinson's sack attempt and flipped the ball to receiver Jeff Janis for a gain of 33. San Diego's defense held for a field goal, the final points of the game.

San Diego tied the game at 17 on its first possession of the second half, with Rivers' 50-yard bomb to wide receiver Malcom Floyd converting a third-and-17 before he found tight end Ladarius Green for a 19-yard touchdown over linebacker Clay Matthews.

The Packers' offense, in a funk since scoring touchdowns on its first two possessions, recaptured the lead with 46 seconds left in the third quarter on Aaron Rodgers' 8-yard touchdown pass to James Jones.

San Diego trimmed the margin to 24-20 with a field goal on the ensuing possession, with Josh Lambo kicking a 32-yard field goal one play after Packers cornerback Sam Shields dropped a potential interception.

The Packers led 17-10 at halftime, scoring their second touchdown on Starks' long run against an overaggressive Chargers defense.

"We have to eliminate the big plays, and that's a big thing," Chargers coach Mike McCoy said. "We have to make teams go the distance. That explosive play, whether it's a run or a pass, we have to do a better job of neutralizing those things."

San Diego put together two good drives in the second quarter, but only one of them resulted in points. On the first, McCoy kept the offense on the field on fourth-and-3 from the Green Bay 12-yard line. Rivers threw a back-shoulder pass to Gates near the goal line, but Gates dropped what might have been the 102nd touchdown catch of his career.

On the next, Allen continued his prolific first half with a 38-yard catch on a deep post, a beautiful toe-tapper for a gain of 16 for a first-and-goal at the 7 and another just short of the goal line on third-and-goal from the 10. On fourth-and-goal on the final play of the half, Rivers looped a 1-yard pass over safety Micah Hyde to receiver Dontrelle Inman.

NOTES: San Diego's Philip Rivers made his 150th consecutive start, the fourth-longest streak by a quarterback in NFL history. ... Packers QB Aaron Rodgers passed 30,000 career passing yards, breaking Johnny Unitas' record for fewest attempts to that milestone. ... Packers RB James Starks' 65-yard touchdown run in the first quarter was the team's longest since DeShawn Wynn's 73-yarder vs. Detroit in the 2008 finale. Starks had the first two-TD game of his career Sunday. ... Chargers RB Melvin Gordon left the game with a lower leg injury, returned and fumbled twice before watching most of the second half. ... Chargers WR Keenan Allen finished the first half with 11 receptions for 128 yards -- the most first-half catches in team history and the most in the NFL since 2012 -- while QB Philip Rivers was 22 of 32 for 211 yards. He had almost as many completions as the Packers ran total plays (24) before the break.