Prater's game-winning kick was his third field goal of the fourth quarter. He also made kicks of 19 and 43 yards.
After Jay Feely's 35-yard field goal tied the score 13-13 with 52 seconds to go, the Broncos needed just three plays to get into position for Prater's game-winner.
Starting from the Denver 20, Adam Weber hit Jeremiah Johnson for a 12-yard gain but his next pass was incomplete. Weber then connected with Greg Orton deep down the right side for a 45-yard gain to the Arizona 32, setting up Prater's final kick.
The Cardinals got the only points of the first half when Michal Floyd scored on a 22-yard pass play from Ryan Lindley early in the second quarter.
Arizona went up 10-0 on Feely's 41-yard third-quarter field goal but Bolden took the ensuing kickoff and started up the middle. He then angled to the right and scored on a run that covered 103 yards.
Denver went up 13-10 on Prater first two field goals before Feely made the score 13-13.