The Cardinals were leading 34-17 and seemingly on the way to a sure win with about 6 minutes remaining, but the Titans charged back with two touchdown catches by Michael Preston and a Rob Bironas field goal to forge a tie.
Arizona's Antoine Cason -- who had returned an interception for a touchdown in the fourth quarter -- came up with another pickoff in the first series of the overtime, returning the ball 16 yards to the Arizona 46-yard line.
Following a 15-yard run by Rashard Mendenhall to the Tennessee 21-yard line, Feely booted the game-winner for the Cardinals (9-5), who nailed down their first winning season since 2009.
Carson Palmer completed 20-of-30 passes for 231 yards with a touchdown and Andre Ellington provided 158 total yards on 10 carries and four receptions.
Tennessee (5-9) fell out of playoff contention despite 402 passing yards and four touchdowns from Ryan Fitzpatrick, who completed 36-of-58 passes with two interceptions.
Kendall Wright amassed 150 yards on 12 catches.