The Packers won 27-24 in over-time against the New England Patriots, who were fielding a third-string rookie quarterback in Bailey Zappe for the majority of the game.
Green Bay trailed 10-7 at the long break after Rodgers had the lowest passer rating (11.2) of any half in any game he has started throughout his career, including a pick-six right on half-time. That was only the fourth pick-six of Rodgers' career and second at Lambeau Field.
Eventually, Rodgers got the Packers off the hook, driving them down the field in over-time to set up Mason Crosby's 31-yard game-winning field goal.
Rodgers finished the game with a completion rate of 60 per cent on 21-of-35 passing for 251 yards, two touchdowns and an interception.
"This way of winning, I don't think is sustainable because it puts too much pressure on our defense," Rodgers told reporters. "Obviously, I've got to play better and will play better.
"I think we're going to have to play a little bit better against starting quarterbacks and if our defense isn't playing as well as they can."
On his poor first-half, Rodgers added: "I settled in and usually don't have two terrible halves, so I kind of returned to the form I expect from myself, and we started moving the football."
The win means the Packers improve to a 3-1 record, with running back Aaron Jones playing a key role with 110 rushing yards on 16 carries.
Green Bay may have wrapped up the win in regulation time when Rodgers found Romeo Doubs with a 40-yard pass in the endzone with 2:02 remaining, but the rookie wide receiver clearly did not secure the catch.
Despite that, Packers head coach Matt LeFleur threw the red flag to challenge what he thought was a touchdown, costing his side a timeout that would have helped his side win in regulation time.
"I'm not too proud of that moment," LaFleur said. "That was an emotional decision, and I think it's a great learning lesson that you can never make those emotional decisions in the heat of battle.
"You know better. You've got to survive the ground. [Packers assistant quarterbacks coach] Connor Lewis was in my ear, he's up in the box and he's in my ear, and he said, 'I don't think so.' And he said that we shouldn't challenge it.
"Just made an emotional decision, and it was almost like throwing a Hail Mary. That could have came back and bit us in the butt."
The Packers next face the New York Giants (3-1) in London on Sunday.