Hurts completed 17-of-23 passes for 207 yards and two touchdowns and ran 10 times for 36 yards and a touchdown while the Eagles defenders denied Cowboys star Dak Prescott in the dying seconds for the victory.
"How about that defense? They played a hell of a game," Hurts said. "Had some adversity but the way they showed up for us in the end... we found a way to win. That's all that matters."
Hurts was limping after being sacked by Micah Parsons late in the second quarter, but he answered any worries about a left knee injury by driving the Eagles for two scores in the third quarter, his touchdown throws of 29 yards to DeVonta Smith and four yards to A.J. Brown.
"For this team, for this city, I'll do anything," Hurts said. "I'm just happy we were able to get a win. That's all that matters in the end."
Prescott, who threw for 374 yards and three touchdowns, threw a seven-yard touchdown pass to Jalen Tolbert in the fourth quarter but stepped out of bounds on a two-point conversion run to create the final margin.
Prescott drove Dallas 11 yards seeking a go-ahead touchdown in the last seconds but a sack, incompletion and penalty set up a last-play throw to CeeDee Lamb short of the end zone to give the Eagles a victory that improved their NFL-best mark to 8-1.
"We just want to continue to build momentum, continue to clean things up, continue to press forward -- continue to grow into the team we know we can be," Hurts said.
Red-hot Baltimore steamrollered visiting Seattle 37-3, improving to 7-2 as Keaton Mitchell ran for 138 yards and Gus Edwards ran for two touchdowns.
In Frankfurt, Germany, Patrick Mahomes threw for two touchdowns as the Kansas City Chiefs beat the Miami Dolphins 21-14.
The Chiefs raced ahead 21-0 before holding off a late Miami fightback.
Patrick Mahomes found Rashee Rice for an 11-yard touchdown pass and hit Jerick McKinnon for a touchdown to cap a 13-play, 95-yard drive for a 14-0 lead.
The Chiefs forced a fumble from former Chiefs receiver Tyreek Hill of Miami and recovered the ball, with Chiefs safety Mike Edwards tossing a lateral to Bryan Cook, who sprinted 59 yards for a touchdown and a 21-0 lead.
Touchdowns from Cedrick Wilson Jr. and Raheem Mostert in the third quarter lifted the Dolphins within the final margin but Miami turned the ball over on downs when quarterback Tua Tagovailoa fumbled a wayward snap.
"I'm always going to blame myself -- I've got to catch the ball," Tagovailoa said. "Can't end the game like that when you have an opportunity against a really good team."
Mahomes, who went 20-for-30 for 185 yards, saluted the Chiefs' defense.
"When we've got a defense like that, I can trust we'll find a way to win football games," Mahomes said.
The AFC West division-leading Chiefs improved to 7-2 while Miami slid to 6-3.
Bengals beat Bills
Cincinnati's Joe Burrow threw for 348 yards and two touchdowns and Joe Mixon ran for another touchdown as the host Bengals beat Buffalo 24-18.
"We played great in the first half," Burrow said. "Had our moments in the second half. Defense stepped up in big spots. Big team win."
Josh Allen's 17-yard touchdown pass to Stefon Diggs and a two-point conversion pass to Diggs with 3:32 remaining lifted the Bills within the final margin.
Mixon, however, ran for a first down in the final minutes to secure the victory.
Buffalo's Damar Hamlin, who suffered a cardiac arrest when hit during a game at Cincinnati in January, was not activated for the Bills for the team's first game back in the venue.
Houston rookie C.J. Stroud threw for 470 yards and five touchdowns, including the late game winner as the host Texans beat Tampa Bay 39-37.
Minnesota took a dramatic 31-28 road triumph over the Falcons behind stand-in Joshua Dobbs, replacing injured quarterback Kirk Cousins.