Rodgers tied the team touchdown pass record that he shared with Matt Flynn and matched the NFL mark for a half set by Oakland's Daryle Lamonica in 1969.
The 190th meeting of the NFL's oldest rivalry turned into an old-fashioned blowout, and Rodgers watched most of the second half from the sideline in a knit cap.
"We just kind of got things going our way," Rodgers said. "The line did a good job of giving me time to extend plays. If you extend plays, you look down the field and there's Jordy Nelson. He made some nice catches."
A night full of milestones included Rodgers' 16th scoring pass of 70 yards or more to break the record he shared with Denver's Peyton Manning and Rodgers' predecessor in Green Bay, Brett Favre. Rodgers looked just fine two weeks after tweaking his left hamstring in a loss to New Orleans.
Both teams were coming off byes. The down time didn't help the Bears, who have lost five of six to drop to 3-6.
Their defense has fallen completely apart.
Embattled quarterback Jay Cutler was on his way to having another night to forget at Lambeau Field with two first-half turnovers. He has thrown 12 interceptions in four career games in Titletown.
Cutler was 22 of 37 for 272 yards. His performance surely won't ease the withering criticism the quarterback has faced back home in Chicago.
Rodgers could seemingly do no wrong.
He connected with tight end Andrew Quarless on a 4-yard scoring strike with 3:53 left in the quarter for a 14-0 lead.
But the misery was only just beginning for the Chicago secondary.
Rodgers found Nelson for a 40-yard touchdown pass with 12:17 left in the second quarter. A screen pass to Eddie Lacy on Green Bay's next possession turned into another catch-and-run for a 56-yard score and a five-touchdown lead.
Nelson had six receptions for 152 yards, while Cobb had 72 yards on four catches. He caught a touchdown for the sixth straight game.
"So much emphasis is put on it," Matthews said about improving defensively. "When we stopped their run and the way our offense was going, it was game over."
Marshall left the game in the fourth quarter with a left ankle injury.
Copyright 2014 by The Associated Press