The Texans led 24-0 after the second quarter, but the Chiefs turned the game on its head, at one point scoring 41 points without reply.
Kansas are the first team in NFL post-season history to win a game by 20 points or more after trailing by a margin of 20 points or more.
Mahomes was the power at the heart of the Chiefs' comeback, throwing for 321 yards and five touchdowns.
— Kansas City Chiefs (@Chiefs) January 12, 2020
For the Texans, Deshaun Watson had 388 yards passing and three touchdowns.
Next up, the Chiefs play the Tennessee Titans for the AFC championship.
They trailed 21-3 at half-time and it looked like a heavy defeat was on the cards.
A spirited comeback, driven in large part by Russell Wilson, saw the Seahawks come close to pulling off a second great turnaround of the night, but ultimately the Packers prevailed.
Lambeau Field has never been a happy hunting ground for Seattle, who have now lost nine in a row in the Packers' home stadium.
As so often this season, defence was the main problem for the Seahawks. Though they twice sacked Aaron Rodgers, Seattle did not manage to force a single turnover.
Rodgers has now passed Dan Marino for eighth on the all-time list of career post-season passing yards.
Green Bay next play the San Francisco 49ers for the NFC championship.