For the first time in franchise history, the Chiefs won a playoff game at home as they defeated the Colts 31-13.
Mahomes threw 278 yards, while also scoring a rushing touchdown.
The 23-year-old quarterback showed his class by penetrating the Colts defensive line at will.
However, the Chiefs’ defence was also key to the win, and didn’t allow an Indianapolis first down until the first two minutes of the second quarter.
They will now host the winner between Sunday night’s mega clash between the Patriots and the Chargers.
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The Patriots, who lost in last year’s Super Bowl against the Philadelphia Eagles, will go into Sunday’s game as slight favourites after having a bye week last week.
But Mahomes insisted that whoever it is, he and his team will be ready.
“It means the world to me,” he said post-game.
“We won this game, and we’ve got two more to go.
“We are focused on whoever we play next.
“It’s going to be a great team.
“And I’m looking forward to playing in front of our home fans.”
The Chiefs suffered defeat against the Patriots when the two teams met earlier in the season in a 43-40 thriller.
The Chargers and Chiefs shared a win apiece through the season, with both games going close. In September the Chiefs came out 38-28 victors, while they lost 29-28 in a tight match in December.
Elsewhere in the NFL playoffs, the Dallas Cowboys and the Los Angeles Rams meet to see who will play the winner of Sunday’s clash between the New Orleans Saints and the Philadelphia Eagles.