The Eagles improved their NFL-best record to 10-1 while the Packers, their playoff ambitions in tatters, fell to 4-8.
"We got the GOAT!" Eagles quarterback Hurts said in a post-game television interview, though he was quick to wish four-time NFL Most Valuable Player Rodgers a speedy recovery.
Rodgers, already nursing a broken thumb, said he suffered a rib injury in the first half, which was aggravated in the third quarter apparently when he absorbed one of three sacks on the night.
"I was just having a hard time breathing and rotating my upper body," Rodgers said. "I was worried about a punctured lung as well, so I wanted to get that checked out. I'll get a scan tomorrow."
Rodgers said his lung was fine, and despite "intense" pain he envisioned playing next weekend "as long as I check out OK tomorrow."
The Packers had trimmed the deficit to 34-23 with a field goal before Rodgers departed.
Backup Jordan Love connected with Christian Watson for a 63-yard touchdown and authored a field goal drive, but it wasn't enough against the formidable Eagles offense.
Hurts piled on 310 total yards, completing 16 of 28 passes for two touchdowns. His 157 rushing yards set the Eagles' single-game record for a quarterback as the team gained a whopping 363 yards on the ground.
Hurts connected with Quez Watkins for a 30-yard touchdown to make it 27-20 at halftime, and pushed the lead to 34-20 midway through the third with a six-yard scoring pass to A.J. Brown.
Elsewhere on Sunday, the suddenly surging Cincinnati Bengals claimed a third straight victory on Sunday as the Miami Dolphins and Kansas City Chiefs both took their win streaks to five games.
The Bengals, who fell to the Los Angeles Rams in last season's Super Bowl, beat the AFC South-leading Tennessee Titans, 20-16, in Nashville.
Quarterback Joe Burrow hit Tee Higgins with a 27-yard touchdown pass in the fourth quarter to secure a fifth win in six games for the 7-4 Bengals.
"This is the kind of game that great teams win," Burrow said. "It's not always going to be pretty. This is the NFL. You're playing really, really good teams on the opposing end.
"You've got to find ways to win, and we're starting to do that."
In Kansas City, the Chiefs notched a 26-10 win over the Rams in a game quarterback Patrick Mahomes called "ugly."
Mahomes threw one TD, Isiah Pacheco ran for another and Harrison Butker kicked four field goals as the Chiefs failed to convert five of their six red-zone scoring chances into touchdowns.
"I felt like we didn't execute at a high level in the red zone," Mahomes said. "I threw a dumb, dumb interception there at the end of the game. But it's a team game. The defense stepped up -- they played great."
Miami's fifth straight victory was a comfortable 30-15 decision against the hapless Houston Texans.
Dolphins quarterback Tua Tagovailoa threw for 299 yards and one touchdown and extended his run without an interception to four games.
The Las Vegas Raiders won a shootout in Seattle in overtime, beating the Seahawks, 40-34.
In Cleveland, Nick Chubb ran in an overtime touchdown to give the Browns a 23-17 comeback win over Tom Brady and the Tampa Bay Buccaneers.
Tampa Bay had led 17-10 going into the fourth quarter after Brady had found Ko Kieft with a five-yard pass in the third.
But with 32 seconds left on the clock, Browns quarterback Jacoby Brissett found David Njoku in the endzone to take the game into overtime.
Trevor Lawrence threw for three touchdowns and 321 yards as the Jacksonville Jaguars upset the Baltimore Ravens, 28-27.
Lawrence found Marvin Jones with a 10-yard touchdown pass with 14 seconds left and then found Zay Jones for the game-winning two-point conversion.
Ravens kicker Justin Tucker missed a 67-yard field goal on the last play, an attempt which would have had to beat his own NFL record field goal distance of 66 yards set against Detroit in September 2021.
