Favre, who is playing his 17th NFL season and turns 38 next month, was credited with a 57-yard completion to Greg Jennings, who ran a slant pattern from the left side. The touchdown, with 2:03 remaining, gave the Packers a 24-21 lead.
Following the touchdown, Favre sprinted down field with his arms in the air and got down on his knees to congratulate Jennings. Favre then picked up his favorite receiver Donald Driver before heading to the sideline where teammates were lining up to hug the new record holder.
Favre zeroed in on yet another career milestone just a week after leading the Packers to a road victory over the New York Giants for his 149th win as a starter - passing John Elway's all-time record.
Favre started his quarterback-record 240th straight game on Sunday, tying him for second on the all-time list with former Minnesota center Mick Tingelhoff. Former Minnesota defensive end Jim Marshall holds the all-time mark with 270 consecutive starts.
Including the playoffs, Favre has started 250 career games.
As he usually does, Favre downplayed talk about personal records and individual achievements earlier this week. Besides, Favre said, Peyton Manning will probably end up breaking the touchdown pass mark in a few years.
"I couldn't tell you how it's looked at," Favre said, when asked about the record earlier this week. "I know it's a lot of touchdowns. But if you play a long time, that means you're playing fairly well."
While there is no single record for quarterbacks that carries the significance of Barry Bonds passing Hank Aaron's career home run record, Packers coach Mike McCarthy said Marino's touchdown mark probably comes closest.
This week Favre said he didn't think the touchdown record was getting anywhere near the hype that Bonds' pursuit of Aaron received over the summer. Then he laughed off any further comparison to Bonds, smiling as he jokingly flexed his forearms to prove he doesn't quite measure up.
Powering the Packers to a 17-14 halftime lead over the Chargers, Favre threw two touchdown passes in the first half.
The first went to his favorite target, wide receiver Donald Driver, who dove and stretched his arms to catch a lob from Favre to put the Packers ahead 10-7 in the second quarter. Favre's 418th career touchdown pass came one play after he flipped the ball underhanded to running back DeShawn Wynn for a first down on third-and-3 at the Chargers' 14.
Favre's second touchdown went to tight end Bubba Franks, allowing the veteran to redeem himself for dropping a potential touchdown pass in the first quarter that forced the Packers to settle for a field goal.
The touchdown to Franks came one play after another classic - but not-so-glamorous - Favre moment. Facing first-and-goal at the Chargers' 5, Favre began to scramble and tried to pump fake - only to watch the ball pop out of his hands for an apparent fumble that was recovered by the Chargers.
A replay determined his arm was in motion when the ball popped out, and the play was ruled an incomplete pass. On second-and-goal, Favre found Franks in the left-front corner of the end zone for his 419th touchdown pass.
Favre, who also is two interceptions shy of tying George Blanda's all-time record of 277, makes no apologies for his high-risk, high-reward style of play over the years.
Given the fact he is also closing in on Marino's career records for attempts and yards passing, Favre said earlier this week it's only logical he would have a lot of touchdowns and interceptions.
"There have been some bad plays, some bonehead plays, whatever you want to call it," Favre said earlier this week. "But a lot of those good ones would not be there if it wasn't for taking a chance. For me, it has been well worth the risk."