Under rookie coach John Fox, the Panthers have employed many blitz schemes and pressured Plummer throughout the game, holding the Cards (3-2) to a pair of field goals until the final three minutes.
"It's incredible," Arizona Coach Dave McGinnis said of Carolina's defense. "That defense is just incredible what they've done. Anytime you see a ball go over the edge, they are all flying out there and they have done that for five weeks."
But on third and seven, Plummer escaped a blitz and hit a wide-open Jones in the flat for the tying touchdown.
Prior to Jones' touchdown, Plummer completed a critical 37-yard pass to Frank Sanders on third and 13 that moved Arizona to the Carolina 48.
Carolina (3-2) appeared to be on the verge of forcing a turnover on Arizona's winning drive when rookie defensive end Julius Peppers stripped the ball from Plummer. But Plummer picked up his own fumble, rolled left and connected with MarTay Jenkins for a 17-yard pass.
"I stepped up in the pocket, went and grabbed it and took off to the left," said Plummer, who led his 19th career comeback. "MarTay made a great catch. That was the key in the game."
"It's just the way the league is," Fox said. "Sometimes you need a little luck. That was a little unlucky. I don't think all is lost. It's obviously hard to lose a game like that late as well as it was a week ago."
After Jenkins' catch, rookie running back Damien Anderson had a pair of 12-yard receptions and Plummer ran for six more on a draw play to put the Cardinals at the Carolina 32.
Following an incomplete pass on third and four, Gramatica kicked the second-longest field goal of his career. Gramatica, who had earlier kicked field goals of 41 and 28 yards, shook off a timeout designed to freeze him and split the uprights.
"The snap was perfect," Gramatica said. "I couldn't have asked for anything better. I had excellent protection. I didn't feel any pressure from anyone. I know it wasn't easy, but when you have everything going so perfectly, it makes it easy. The offense stuck it through. They worked so hard to get there with no timeouts."
"He's Jake Plummer," said McGinnis about the fourth quarter comeback. "He's our quarterback and that is exactly why he is here. There is no die in this. Believe me, if you had been in this locker room at halftime and been on that sideline, everybody was up."
Arizona is above.500 after five games for the first time since 1991. The Cardinals were able to get off to their best start in 11 years without their top two running backs.
Thomas Jones was inactive with an ankle injury and backup Marcel Shipp , who scored a pair of touchdowns last week, did not play with a sprained ligament in his knee.
Arizona's wideouts did not offer much help. David Boston, who had seven catches for 127 yards in last season's 30-7 win over the Panthers, had three catches for 43 yards and was unable to catch a pass on third down in the back of the end zone midway through the fourth.
Carolina also had trouble moving the ball and committed four turnovers. Its final turnover led to Arizona's tying drive as Rodney Peete was intercepted by cornerback Coby Rhinehart deep in Cardinal territory.
Running back Lamar Smith also fumbled twice for Carolina, which did little after Peete's 31-yard touchdown pass to Isaac Byrd late in the first half.
"They're a hard hitting team," Fox said. "I thought that they played very hard. It's something that they've been able to do in their wins. We came up short in that area. We can't afford to do that. Again, we finished minus in the turnover margin this week and I think that has a lot to do with losing".
Peete completed 20 of 34 passes for 196 yards, while Plummer was 18 of 40 for 221 yards.