Mahomes, who rolled his ankle in a win over the Raiders last week, came up limping after he managed to escape pressure in the pocket and flip a seven-yard touchdown pass to Samaje Perine that pulled the Chiefs level at 17-17 early in the fourth quarter.
He needed help to get to the sideline, but after treatment in the medical tent he returned to hit DeAndre Hopkins with a five-yard touchdown pass that put the reigning Super Bowl champions up 24-17 with 4:17 remaining.
But Tampa Bay responded, quarterback Baker Mayfield piloting a 10-play, 71-yard drive capped by a one-yard touchdown pass to Ryan Miller.
The Bucs opted not to go for a two-point conversion and the lead, and the extra point kick tied it at 24-24.
Kansas City’s final drive in regulation stalled, but they got the ball to start overtime and Mahomes directed a methodical 10-play march to the game-winning score.
Hunt, behind blockers Wanya Morris and Creed Humphrey, rushed for 106 yards, Mahomes crediting his persistence with wearing down the Tampa Bay defense.
“Obviously we were doing some good early in the game, but we couldn’t finish drives,” Mahomes said.. “And then Kareem took it on himself … he took it running again and we were able to do it again.”
Travis Kelce had two catches on the game-winning drive and finished the night with 14 catches for 100 yards.
Hopkins, in his second game since arriving in Kansas City via a trade from Tennessee, had eight catches for 86 yards and two touchdowns, the first a one-yarder that put the Chiefs up 10-7 in the second quarter.
Mayfield connected on 23 of 31 passes for 200 yards and two touchdowns and Rachaad White — who grew up in Kansas City — rushed for another touchdown for the Bucs.
The game was the latest renewal of the rivalry between Mahomes and Mayfield, which stretches back to their college days.
Mahomes and Mayfield combined in a wild college football showdown in 2016 that saw Mayfield’s University of Oklahoma take down Mahomes and Texas Tech in a clash that finished 66-59.
This season, their fortunes have diverged, and as the Chiefs continue their unbeaten run toward a shot at a third straight Super Bowl title the Bucs have now fallen to 4-5 with four defeats in their last five games.
Mahomes downplayed his ankle injury after the game, saying he expected to be ready when the Chiefs host Denver on Sunday.
“You always fear the worst,” he said. “But as I got some time it started feeling better. We’ve got a short week, but we’ll rehab it up and I’ll be ready to go next week.”