However, the Cowboys (2-1) answered back when shortly before the halftime break when Prescott finished off a 10-yard run with a head over heels flipped into the end zone with 1:11 left in the second quarter.
The third quarter ended 14-14 after Prescott found Dez Bryant with a 15-yard scoring pass for Dallas and Carson Palmer mirrored that distance when he found Larry Fitzgerald to knot the game.
Prescott and the Cowboys then pulled away in the fourth quarter after Brice Butler pulled down a 37-yard pass inside the end zone and Ezekiel Elliott ran home from 8-yards to polish off the game, as the travelers outscored Arizona 14-3 in the last quarter.
Prescott finished 13 of 18 for 183 yards without an interception, while Butler took two catches for 90 yards and his TD and Elliott ran for 80 yards and his TD for Dallas, which bounced back from the 42-17 defeat to Denver in Week 3.
“He just kept battling,” Dallas coach Jason Garrett said of his QB.
“He kept making good decisions. Obviously he made some good plays, big-time throws, but as much as anything else he’s got an amazing spirit and our players follow him.”
Meanwhile, Carson Palmer went 29 of 48 for 325 yards and two touchdowns for the Cardinals (1-2), who outgained Dallas 332-273, but had only 49 rushing yards.
“There running game was dependent on me,” Cardinals coach Bruce Arians said, as he took the blame.
“I loved what we had passing the ball. We just had to protect better.”
Larry Fitzgerald collected 13 of 15 targets to tie a career high for receptions for 149 yards and a touchdown and Jaron Brown also had a scoring reception for Arizona in the defeat.
“That’s Fitz. It’s Monday night,” Arians said. “He’s a money player.
“It was a great performance by him. It’s a shame we couldn’t play better around him.”