Even in his 300th career game, the 42-year-old Vinatieri continues to perform as if in the prime of his career.
Vinatieri warmed up before the game by nailing 60-yard kicks. His game-winner also might have been good from 60.
McAfee, the punter and holder on extra points and field goals, made it sound as if Vinatieri is even older.
''The guy is wearing Depends and he's just knocking down game-winners every week,'' McAfee said. ''It's incredible to watch. I'm lucky to be teammates with that guy.''
Vinatieri is only the 10th player in NFL history to play in 300 games. The game-winning field goal was the 26th of his career in the final minute of regulation or in overtime.
''Each one is exciting in its own way,'' Vinatieri said of his long list of game-winning kicks. ''I'm just excited we had the opportunity to get the score tied back and I had the opportunity to help the team win the game.''
With the comeback win, the Colts (5-5) remained in a first-place tie with Houston in the AFC South. They have recovered from three straight losses with back-to-back wins over Denver and Atlanta.
The Falcons (6-4) have lost four of their last five following a 5-0 start.
Matt Ryan set a season high with three touchdown passes, but he also threw three interceptions. Most costly was a pass from the Falcons 1 that was intercepted by D'Qwell Jackson and returned 6 yards for a tying touchdown early in the fourth quarter.
Ryan said he did not see Jackson ''popping back out off the line of scrimmage.''
''It is just a play I cannot make,'' Ryan said. ''In critical situations, you cannot turn the ball over, and I have to be better than that.''
Atlanta linebacker Paul Worrilow ended the Colts' first possession with an interception. Worrilow recovered Frank Gore's fumble to end the Colts' second possession. The Falcons could not turn either turnover into points.
Here are some more things to know about the Colts' comeback win:
REMEMBERING RODDY: Roddy White, who holds most of the Falcons' career receiving records, had seemed like the forgotten member of the offense this season with only 17 catches through nine games. Following the bye week, he suddenly re-emerged.
Ryan threw to White on each of the team's first three plays. White had four catches for 24 yards on a season-high nine targets.
GAME-CHANGING PUNT: Vinatieri tried to share the postgame spotlight with McAfee, who set up Jackson's interception by having a 50-yard punt downed at the 1-yard line. ''I don't think there was a bigger play,'' Vinatieri said. Ryan's crucial interception came on first down from the 1.
INJURY UPDATE: Falcons running back Devonta Freeman had a strong start, with three carries for 43 yards, before leaving with a concussion in the first quarter. Wide receiver Leonard Hankerson, who was active after missing three games with a hamstring injury, limped off the field after appearing to aggravate the injury late in the game. Colts cornerback Vontae Davis also suffered a hamstring injury.
ME AND MY SHADOW: Davis began the game shadowing Julio Jones. The coverage didn't affect Jones, who had nine catches for 160 yards as he again showed he can't be stopped by one defender. The Colts let their other starting cornerback, Greg Toler, try to contain Jones in the second half.
2 TDS FOR DIMARCO: Atlanta fullback Patrick DiMarco had only one career scoring catch in four seasons before having two touchdown receptions in the first half. He had a 15-yard catch for the Falcons' first touchdown and added a 1-yard scoring catch in the second quarter.
AP NFL website: www.pro32.ap.org and AP NFL Twitter feed: www.twitter.com/AP-NFL