GREEN BAY, Wis. -- Aaron Rodgers didn't need Davante Adams, and he barely needed his other two banged-up starting receivers to put together his best game of the season and his most productive performance under first-year Green Bay Packers coach Matt LaFleur.

Six touchdowns later, Rodgers led the short-handed Packers to a 42-24 victory over the Oakland Raiders on Sunday at Lambeau Field. Rodgers threw for five of them. His fourth touchdown was also the 350th of his career, the ninth quarterback in league history to reach that mark.

He also ran for one, and unlike his counterpart on the Raiders, Derek Carr, there was no pylon fumble to ruin the play.

In the process, Rodgers became the first NFL player with five touchdown passes and a rushing touchdown in the same game since Mark Rypien in 1991.

"I feel like this has been coming, I really do," Rodgers said. "I feel like we've been building and I've been feeling a lot more comfortable, and Matt's been feeling more comfortable with him calling it for me and feeling when I'm in that rhythm and when to be aggressive and when to pull back."

Without Adams (turf toe) for the third straight week and with his other two starting receivers Marquez Valdes-Scantling and Geronimo Allison on limited snap counts after they were surprisingly active, Rodgers more than made it work.

And he did it without throwing his first completion to a receiver until the 8:04 mark of the second quarter. By then, he already had 80 passing yards to running backs. The backs finished with 102 receiving yards.

Rodgers finished 25-of-31 for 429 yards -- the fourth-highest total of his career -- giving him the maximum possible passer rating of 158.3. He's the first Packers quarterback to finish with the max passer rating (minimum 10 attempts) in the Super Bowl era.

"I still don't understand how they put that rating together, but it does sound pretty good," Rodgers said.

In many ways, this was LaFleur's new offense at its core.

Running backs Aaron Jones and Jamaal Williams each caught touchdown passes on plays designed to create mismatches, while fullback Danny Vitale caught passes of 21 and 22 yards. Rodgers had eight completions of 20 yards or more, tying a career high, and they went to six different players -- the first time in his career he's had that many plays of that length to that many different players.

Oh, there were receivers who got into the mix eventually.

Jake Kumerow caught the first non-running back touchdown of the day on the game-swinging sequence after Carr fumbled while trying to dive for the pylon with 1:49 left in the first half. Rodgers answered by hitting the fan-favorite Kumerow down the right sideline for a 37-yard score that left many at Lambeau wondering how -- or if -- he stayed in bounds.

Valdes-Scantling caught two passes for 133 yards. His first was a 59-yard catch on play-action to open the third quarter and set up Rodgers' 3-yard scoring run. His other was a 74-yard catch-and-run touchdown that allowed Rodgers to turn things over to backup Tim Boyle to finish.

Last week's hero against the Lions, Allen Lazard, had a 26-yard catch as part of a three-catch, 42-yard game.

Tight end Jimmy Graham had his moments, too. He caught Rodgers' fourth touchdown of the game, a 3-yarder, as part of a four-catch, 65-yard day.

"That's how you want it to look," LaFleur said. "This is the National Football League, so it's not going to be like that every week. But I just thought our guys, coming off six days, I thought they were locked in. They knew the game plan inside and out, and they went out there and executed it. I'm just really proud of the effort and the execution of our guys."

If their goal was to survive until the Oct. 27 game at Kansas City, when they hope to get Adams back, then it should be considered a success. They're 6-1 heading into the Sunday night game against the Chiefs, who are expected to be without reigning NFL MVP Patrick Mahomes.

"Yeah, I can promise you we need him, and we're a better offense with [number] 17 on the field," Rodgers said. "We've just been spreading it out a little bit more and guys have been stepping up. I think it's given everybody a chance to see the talent that we have with Jake Kumerow and Allen Lazard -- guys who don't get a lot of playing time when our first three are healthy. Those guys are talented players. They can really play. And I thought Jimmy had his best performance today, which was great to see. So it's given guys more opportunities. You know, 17 is so dynamic. He's open on so many plays, and I think without him there, we've had to scheme up plays for other guys, and guys have made plays when their number's been called."