Eric Berry, who already had an interception return for a touchdown, picked off an attempted two-point conversion pass from Matt Ryan in the fourth quarter and raced 99 yards to give the Chiefs a 29-28 victory.
"I was an opportunity to make something happen and was going to try to take advantage of it," said Berry, who has come back from cancer.
"It's a lot worse than 'oh darn' ... not sure you can print it," Ryan said of his reaction to the decisive pick.
The Falcons had just taken the lead on a 5-yard TD pass from Ryan to Aldrick Robinson with 4:53 remaining when Berry stepped in front of rookie tight end Austin Hooper and raced down the field untouched.
"I was just glad Eric was there," Kansas City coach Andy Reid said. "He knows how I feel about him."
The Chiefs (9-3) also scored two touchdowns on fourth-down plays, including a fake punt, as they stunned the Falcons (7-5).
Albert Wilson, who played in college at the Georgia Dome for Georgia State, raced 55 yards with a short direct snap on the fake punt and Berry, an Atlanta native, had a 37-yard interception return for a touchdown pick.
Berry's TD pick was the Chiefs' sixth defensive touchdown this season.
"He watches so much film, it's ridiculous," linebacker Tamba Hali said of Berry. "He prepares so much that it's no surprise when he makes big plays. ... He just took the ball (on the two-point try) and was off."
Alex Smith completed 21 of 25 passes for 270 yards and a Chiefs touchdown, finishing with a 124 QB rating. Tight end Travis Kelce had eight receptions for 140 yards -- his third straight game going past that mark.
Ryan completed 22 of 34 passes for 297 yards and a touchdown, but both of his picks were also turned into scores.
Wilson's TD on a fourth-and-1 fake punt, came early in the third quarter after the Falcons called a timeout when the Chiefs kept their offense on the field as if going for it that way.
"I was just worried about dropping the snap," the wide receiver said. "When I heard the call, I was ready. We've practice it."
The Falcons failed on a fourth-down play from the 10-yard line in the third quarter before Devonta Freeman scored his second touchdown of the game from a yard out early in the fourth. Ryan's two-point conversion attempt was incomplete.
Berry picked off a Ryan pass over the middle intended for Taylor Gabriel and returned it for a score with 37 seconds left in the second quarter to put the Chiefs ahead.
Matt Bryant, though, kicked a 59-yard field goal as time expired to get the Falcons within 20-16 at halftime. It tied for the longest field goal in team history.
The Falcons got points the first three times they had the ball, but had to settle for field goals of 22 and 21 yards by Bryant after Freeman scored from a yard out on the game's first possession.
Spencer Ware caught a 3-yard touchdown pass from Smith on a fourth-down play in the second quarter after capping the Chiefs' first possession with a 3-yard run. Cairo Santos had his first extra-point attempt blocked.
"It's frustrating to lose a game like this," Falcons defensive end Jonathan Babineaux said. "You only get 16 games (in the regular season). "You don't want one of them to slip away."
Falcons LT Jake Matthews was forced out of the game in the second quarter because of a left knee injury. T Tom Compton replaced the 2014 first-round draft choice.
With DE Adrian Clayborn (knee) out, DE/DT Ra'Shede Hageman was active for the Falcons after not dressing for three of the previous four games and blocked a Chiefs extra-point attempt.
LB Dee Ford (hamstring) returned for the Chiefs after missing a game and DT Dontari Poe (back spasms) played despite sitting out practice all week.
CB Steven Nelson started in place of Chiefs CB Phillip Gaines (knee).
Chiefs WR Jeremy Maclin (groin) was inactive for his fourth straight game.
The Chiefs have a short week coming up, playing the Oakland Raiders at home on Thursday.
The Falcons travel to the West Coast for the third time to play the Los Angeles Rams next Sunday.