The Denver Broncos hopes of joining the Chargers in the post-season suffered a blow though as they lost an overtime thriller to the Cincinnati Bengals 30-24.
The Patriots, who suffered a sixth straight loss, were booed off the field by the remaining fans at Gillette Stadium as they fell to 3-13 on the season.
But for the Chargers it was a job well done as the confident Herbert ensured a second post-season place in three seasons with another accomplished quarterback display.
Herbert completed 28 of 38 passes and threw for 281 yards against a Patriots defence that caused few issues against the passing game.
The Chargers took the lead late in the first quarter thanks to a beautiful 23-yard Herbert pass, superbly caught by the diving Derius Davis.
After a Cameron Dicker field goal early in the second, Herbert found rookie receiver Ladd McConkey at the back of the end-zone with a pinpoint pass to make it 17-0.
Patriots rookie quarterback Drake Maye had been forced out of the game in the first quarter after suffering a hit to the head by Cam Hart when running down the sideline.
But Maye, who had been cleared to return for the second quarter, showed he was in good shape with a fine 36-yard touchdown pass to DeMario Douglas to give the Patriots some hope.
But the Chargers ran away with the game, with Herbert again connecting with McConkey - this time with a 40-yard pass down the middle. A two-yard rush from J.K Dobbins in the fourth completed the rout.
Herbert's performance meant he set a new record for the most passing yards in the first five years of an NFL career - passing Peyton Manning's tally of 20,618 yards.
But the quarterback, who has yet to win a playoff game, was quick to give credit for his achievement to his team-mates.
"It says so much about the guys we had catching those passes and a great offensive line giving me the time to get the ball off and (the defence) getting me the ball back," he said.
"I couldn't have done it without them," he added.
Broncos denied
The Broncos headed to Cincinnati knowing that a win would secure them the final AFC place in the playoffs but they now must beat the defending Super Bowl champions, the Kansas City Chiefs, to be sure of extending their season.
The game was 10-10 after a largely attritional first-half but the contest came alive when Bengals quarterback Joe Burrow found Tee Higgins with a 12-yard touchdown pass.
Denver responded in impressive fashion with a magnificent 51-yard hurl from their rookie quarterback Bo Nix to Marvin Mims.
After back-to-back turnovers, Burrow's one-yard rushing score made it 24-17 with 1:29 to go.
But Nix delivered again - throwing high to Mims in the end-zone and despite double coverage, the receiver came down with the ball to tie the game with eight seconds remaining.
Neither side was able to score on its first possession in overtime and the Bengals then worked their way to a 33-yard field goal position but backup kicker Cade York's effort struck the upright.
Denver failed to take advantage of that let-off, however, as they were forced to punt and this time the Bengals found the decisive score - Higgins brilliantly bringing in a 31-yard pass from Burrow on a drive capped when the pair connected again for the three-yard game-winning touchdown.
The fourth straight win for the Bengals means they remain alive going into the final week of the regular season having recovered from a 4-8 record.
Rams hang on
The Los Angeles Rams inched closer to clinching the NFC West division title with a 13-9 victory over Arizona.
Rams cornerback Ahkello Witherspoon was the hero, coming up with an interception after a Kyler Murray pass deflected off intended receiver Trey McBride and squirted into the air to seal the win.
Trailing 10-0 at half-time, Arizona had cut the deficit to 10-9 early in the fourth.
Joshua Karty's second field goal of the game put the Rams up 13-9 with 6:33 to play.
Puka Nacua had 129 receiving yards and Kyren Williams scored the only Rams touchdown on a one-yard rush in the first quarter.
Los Angeles quarterback Matthew Stafford passed for 189 yards and Murray passed for 321 yards and one touchdown on a night when both teams struggled to score.
The Rams host their division title rivals Seattle in their regular-season finale next weekend. However, if multiple results fall their way they could clinch the division crown before then.