Rodgers completed 25 of 31 passes for 305 yards as the visiting Packers dominated the contest at Levi's Stadium in Santa Clara, California to improve to 6-2 overall.
The 49ers have been hit hard by injuries to key players and to make matters worse they lost additional players this week to Covid-19 protocols, which at one point put Thursday's clash in jeopardy.
"It was one of those games, a little bit strange but fun to come out on top," said Rodgers. "We have a lot of pride and we went out and executed the way we expected to."
The 49ers shut down their Santa Clara workout facility on Wednesday after receiver Kendrick Bourne's negative test result. He was placed on the Covid-19 list.
San Francisco was already missing a number of key players, including quarterback Jimmy Garoppolo (ankle sprain) and tight end George Kittle (foot), Deebo Samuel (hamstring), Raheem Mostert (ankle), Tevin Coleman (knee) and Jeff Wilson (ankle).
Green Bay was dealing with coronavirus issues of their own as Jamaal Williams and AJ Dillon were out due to Covid-19 protocols.
"It was a different game. The teams were depleted on both sides of the ball," said Rodgers. "I don't feel sorry for anybody in this league. That's the way it goes."
Davante Adams had 10 receptions for 173 yards and one touchdown for Green Bay, who have scored at least 30 points in all six of their wins this season. Adams also had more than 150 receiving yards for the third time this year.
Marquez Valdes-Scantling caught two touchdown passes, and Marcedes Lewis also had a scoring reception for the Packers, who put up 405 total yards.
Nick Mullens, who started in place of Garoppolo, had 291 yards and one touchdown on 22-of-35 passing but also tossed an interception for San Francisco.
The Packers controlled the ball for over 36 minutes while moving a game ahead of the Chicago Bears (5-3) in the National Football Conference's North Division standings.