Former University of Utah star Alex Smith picked apart the Packers. He was 20-for-26 for 211 yards and two touchdowns, and Frank Gore rushed for 112 yards and a touchdown.
49ers linebacker Ahmad Brooks said the 49ers' victory could be an "eye opener" for the Packers, and a sign that the 49ers are poised for another big playoff run.
"Maybe we'll see them again in the NFC championship," Brooks said.
Facing a Packers team that lost only once in the 2011 regular season was a tough opening road test, but the 49ers were more than ready.
"We were just tremendously on it today, and that was a big part of our victory," 49ers coach Jim Harbaugh said.
Things went so well for San Francisco that when David Akers tried a 63-yard field goal at the end of the first half, it bounced off the crossbar and then kept going through the uprights to tie an NFL record.
"When you hit the goal post at any part, it usually makes that horrific noise and then it usually bounces back," Akers said. "This time it got there. It was a sweet bounce. It was definitely a once-in-a-lifetime type of a deal."
Moss scored on a 14-yard reception in the second quarter. He then turned his back to the crowd and pointed to the name on his jersey, opting for a more subdued celebration than the now-notorious fake mooning motion he made toward fans at Lambeau during his Minnesota Vikings days.
"He had a lot of juice, he blocked well," Harbaugh said. "He got open and he was a great big target in there."
The Packers came into their opener with hopes that a rebuilt defense and improved running game could help get them back to the Super Bowl after coming up short in the playoffs last season.
"They've got a great defense," Rodgers said. "You've got to give them credit. They've got some of the top guys in the league at their position."
Rodgers finished the game as the Packers' leading rusher, with new addition Cedric Benson gaining just 18 yards on nine carries.
The Packers don't have long to prepare for their next game, Thursday night at home against the division rival Chicago Bears.
"It's one game," Rodgers said. "This is a team that was in the NFC championship last year. It's a good team. Hopefully we see them down the road in the playoffs."
Rodgers finished 30-for-44 for 303 yards with two touchdowns and an interception, but the 49ers held him in check until late the in the game. Jermichael Finley had a 1-yard touchdown for the Packers.
Monday night football
P Cincinnati at Baltimore, 5 p.m., ESPN
• San Diego at Oakland, 8:15 p.m., ESPN