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Philadelphia looked to edge back in front in the second quarter, but Josh Huff fumbled the ball to give possession back to the hosts.
There was a head-to-head collision between Patrick Peterson and Maclin shortly before half time, and while the Eagles receiver returned to the game after undergoing concussion tests, Peterson did not feature after the break.
The visiting team were back in front just moments into the third quarter when Carson Palmer completed a pass down the centre to Fitzgerald, who dodged a string of tackles before sprinting to the endzone for an 80-yard touchdown.
Philadelphia were back ahead by the end of the quarter though, as Cody Parkey edged them back ahead with a field goal before Maclin scored his second touchdown of the day, taking a 54-yard Foles pass at the back of the endzone.
Chandler Catanzaro kicked the Cardinals back onto level terms after Michael Floyd failed to keep his feet in bounds for a touchdown, breaking the league record for the longest streak without missing a field goal for a rookie kicker.
Parkey briefly nudged the Eagles back in front with another kick, but a well-timed long pass from Palmer found Brown near the halfway line, and the rookie ran the ball all the way to the endzone for a 75-yard touchdown.
Foles tried hard to set up a touchdown for the Eagles in the final seconds, connecting with Maclin to move into the red zone, but Tyrann Mathieu batted the ball down in the endzone before Jordan Matthews was pushed out of bounds to prevent him making the catch, sealing the win for Arizona.
The result leaves the Cardinals at the top of the NFC West with a 6-1 record, while the Eagles fall to 5-2.