Donald Driver did the rest.
The veteran receiver's rambling 61-yard catch-and-run for a touchdown broke the game open in the third quarter, and the Packers went on to beat the San Francisco 49ers 34-16 at Lambeau Field on Sunday.
Greg Jennings caught six passes for 122 yards and a pair of touchdowns for the Packers (8-4), who picked up a critical victory as they make a push for the playoffs in the final month of the season.
Rodgers was 21 of 30 for 298 yards with three touchdowns and no interceptions.
Vernon Davis had 126 yards receiving and a touchdown for the 49ers (4-8), who came into Sunday's game with playoff hopes despite their disappointing record.
It was a wintry day at Lambeau, with temperatures in the 20s and a stiff, steady 16-mph wind.
The conditions seemed to impede the Packers' passing game early as Rodgers was uncharacteristically off target, missing Driver in the end zone in the first quarter and failing to convert an open third-and-long throw in the second quarter because the ball bounced off a defender's helmet.
But Rodgers found his mark midway through the second quarter, when a defender jumped offside to give him a free play -- and Rodgers delivered a deep strike to Jennings for a 57-yard touchdown, giving Green Bay a 7-6 lead.
Rodgers really found a rhythm after halftime.
Green Bay was leading by 1 in the third quarter when Driver left San Francisco's defense in his dust, catching a sharp pass from Rodgers and bouncing off a series of potential tacklers on his way to the end zone.
The 49ers answered Driver's touchdown with a field goal to cut the Packers' lead to 21-16, but Rodgers delivered a deep strike to Jennings to put the Packers in scoring position. Rodgers found Jennings again for a touchdown three plays later, giving Green Bay a 28-16 lead.
The 49ers were without running back Frank Gore, who fractured his hip in a victory at Arizona on Monday night.
49ers quarterback Troy Smith was 10 of 25 for 194 yards, including a 66-yard touchdown to Davis to cut the Packers' lead to 1 just before halftime.
Smith got the 49ers off to a good start with a pair of drives for field goals by newly signed kicker Jeff Reed.
After Rodgers' touchdown to Jennings, Green Bay extended its lead to 14-6 when Rodgers flipped the ball to Brandon Jackson for a big gain to set up first-and-goal. John Kuhn then plunged in for a touchdown -- a critical conversion for a team that struggled in short yardage situations in a loss at Atlanta the previous week.
But Smith found Davis wide open in the middle of the field and Davis ran 66 yards for a touchdown to cut the Packers' lead to 14-13 at the half.