Three of the past four times they met, the game wasn't decided until the last play, twice going to overtime.
The Cardinals won all four of those games, but the Cowboys stopped the streak with a 28-17 victory on Monday night at University of Phoenix Stadium.
Dak Prescott threw two touchdown passes, Ezekiel Elliot ran for a score, and the Cowboys, who gained just 57 total yards in the first half, rebounded from a humbling 42-17 loss in Denver the previous week.
"Dak was an animal today," Elliott said. "He came out there and made some big plays. Sometimes he has to use his feet to get out of the pocket and make those downfield throws, but he played amazing."
The Cardinals fell to 1-2, but as disappointed as Bruce Arians was with the Monday night result, the Arizona coach found a positive.
"When you look at the big picture," he said, "we're one game out of first place in our division and we have a big division game next week (at home against the 49ers). This one is over with, and we'll learn from it."
The Cowboys were leading 21-14 after Prescott found Brice Butler in the end zone for a 37-yard touchdown pass with just under 12 minutes left. Prescott was under pressure, rolled out to his right and hung the pass up in the air. Butler outleaped cornerback Justin Bethel for the ball and hauled it in for the score.
"It was just good to have that happen tonight," Butler said of his touchdown grab, "(Dak) saw me and he threw it up there, and I had to go and get that thing. Old-school scramble. When you see the quarterback go to the right, you go to the high pylon."
"We have to finish better," Bethel said. "It was a game that came down to the fourth quarter and we had a chance to win, but we couldn't pull it out at the end like we needed to."
The Cardinals looked as if they were on their way to tying the game, but a 16-play drive resulted in a 37-yard field goal from Phil Dawson.
Prescott and the Cowboys made the Cardinals pay for that as the Dallas quarterback rolled out to his right once again and found Butler again for a 53-yard completion.
Elliott capped things with an 8-yard touchdown run with 4:57 remaining. A week after finishing with just 8 yards on nine carries against the Broncos, he ran for 80 yards on 22 carries against the Cardinals.
Six minutes into the third quarter, Prescott hooked up with wide receiver Dez Bryant to give the Cowboys their first lead of the game at 14-7. Elliott broke a 20-yard run on the previous play to give the Cowboys the ball at the Arizona 15-yard line before Prescott found Bryant over the middle.
Initially, it appeared the Cardinals had him stopped well short of the end zone, but Bryant kept moving the pile, and after a second, third and fourth effort, got the ball to cross the plane for the touchdown.
"We just have to make sure we rally to the ball carrier a little bit better in that situation," said Cardinals cornerback Patrick Peterson, who was playing zone coverage and wasn't shadowing Bryant one-on-one on that particular play.
The Cardinals needed their star wide receiver to match the effort, and Larry Fitzgerald, 34, obliged. He hauled in a 37-yard bomb from Carson Palmer down the left sideline and two plays later caught a 15-yard touchdown to tie the score at 14.
The catch, Fitzgerald's 10th of the game at that point, gave him 98 receiving yards, moving him ahead of Marvin Harrison (14,580) for eighth place on the league's all-time receiving yards list. He finished the night with 13 catches for 149 yards and one touchdown.
"That's Fitz. That's Monday night," Arians said. "He's a Monday player."
Palmer was 29 of 47 for 325 yards and two touchdowns with no interceptions. Prescott, meanwhile, completed 13 of 18 passes for 183 yards with no interceptions.
The score was tied 7-7 at halftime, although the Cardinals were lamenting the fact they weren't ahead by at least a touchdown.
They scored on their first possession, completing an eight-play, 82-yard drive when Palmer hit wide receiver Jaron Brown for a 25-yard strike over the middle in the end zone. Palmer was 5 of 5 for 79 yards in the series with 20-yard completions to tight end Jermaine Gresham and running back Andre Ellington.
After forcing the Cowboys to punt, the Cardinals mounted another long, time-consuming drive. Palmer completed each of his first six passes, including a 17-yarder to Ellington, before throwing the ball away to snap his streak of 11 straight completions.
He thought he had a 10-yard touchdown throw to Brown, but the play was negated by a holding penalty on right tackle Jared Veldheer. The Cardinals had to settle for a field-goal try, but kicker Phil Dawson's 36-yard attempt was wide right. After a drive that nearly lasted nine full minutes, Arizona came away with nothing.
It was Dawson's third missed field goal in three games and the turn of events stung the Cardinals.
"You get all excited because you think you have a touchdown," Palmer said. "Again, we put ourselves in a long situation, a third-and-long, and it's just very difficult against a smart defense. When you do that, like we did a number of times, it's difficult to convert those."
The Cowboys, who had accounted for only 4 yards of offense in their first two possessions, scored the fourth time they had the ball when Prescott called a keeper on first-and-goal at the 10-yard line and leaped toward the end zone, flipping end over end as he was met by the goal line by Arizona defenders Antoine Bethea and Bethel.
The Cardinals outgained the Cowboys 152 yards to 52 in the first half.
The Cowboys were playing without two starters on defense -- cornerback Nolan Carroll (concussion) and inside linebacker Anthony Hitchens (knee). The Cardinals were once again without left tackle D.J. Humphries (knee), left guard Mike Iupati (triceps), inside linebacker Deone Bucannon (ankle) and wide receiver John Brown (quadriceps).
Before the game, players, owners and executives from both teams locked arms in a show of solidarity during the national anthem. The Cowboys players and management, including owner Jerry Jones, knelt briefly before the large U.S. flag that covers the playing surface was unfurled.
That drew some boos from the crowd, but the Cowboys contingent quickly rose to its feet before the anthem began. Anthem singer Jordin Sparks had a reference to a Bible verse written on her hand: "Speak up for those who cannot speak for themselves, for the rights of all who are destitute." Proverbs 31:8-9.
"I think this team, this organization, players, coaches, staff, everyone did the right thing," Prescott said of the Cowboys' pregame decision. "We came together. We had a lot of dialogue. Talked about what we wanted to do, just as a sign of the unity we want to bring in this country and just help everything that's going on right now. I think we did a great job."
NOTES: Dallas made its 79th appearance on "Monday Night Football," second most in NFL history behind the Miami Dolphins (82). ... With a 4-yard reception in the first quarter, Cardinals WR Larry Fitzgerald extended his consecutive games with a catch to 198 games, the third-longest such streak in league history behind Jerry Rice (274) and Tony Gonzalez (211). ... Cowboys WR Dez Bryant appeared in his 100th NFL game. ... Earlier Monday, the Cardinals elevated TE Ricky Seals-Jones from the practice squad to the 53-man active roster and released LB Phil Wheeler. It was the third time that Wheeler, a 10-year veteran, was released since originally signing with Arizona on July 27.