Earlier in the day, the Chargers (9-7) got the help they needed when Miami and Baltimore both lost. San Diego has won four straight and five of six heading into a wild-card game next weekend at AFC North champion Cincinnati.
The Chiefs (11-5) go into the playoffs having lost five of seven. They play at AFC South champion Indianapolis, which won 23-7 in Kansas City last week.
With the Chargers on the verge of an embarrassing collapse against a team with nothing to play for, Philip Rivers threw a 6-yard touchdown pass to Eddie Royal early in the fourth quarter and Novak kicked a 22-yard field goal to tie it with 3:21 left in regulation
Kansas City kicker Ryan Succop was wide right on a potential game-winning, 41-yard field goal try with 4 seconds left in regulation.
The Chiefs lost the overtime coin toss and the Chargers, who stunned their AFC West rivals 41-38 in Kansas City on Nov. 24, elected to receive.
The winning drive was kept alive by a 2-yard gain by Pro Bowl safety Eric Weddle on a fake punt on fourth-and-2 from the Chargers 28.
With backup Chase Daniel starting in place of quarterback Alex Smith, the Chiefs took their biggest lead, 24-14, on Succop's 46-yard field goal with 7:27 left in the third quarter. The drive was set up by Dexter McCluster's 32-yard punt return to the Chargers 35.
Rivers then rallied San Diego to 10 points on consecutive drives.
The Chiefs took the game's opening kickoff and needed only five plays before Knile Davis scored on a 17-yard run.
The Chargers came right back on a five-play drive of their own and scored on Rivers' 22-yard pass to Ladarius Green. The drive included a 44-yard run by Ryan Mathews, who stiff-armed a Chiefs defender for a few extra yards.
After being forced to punt, the Chiefs got the ball right back when Ron Parker intercepted Rivers at the Chargers 23. Rivers yelled at rookie wide receiver Keenan Allen as they walked to the sideline. The drive was kept alive on an encroachment penalty against rookie linebacker Manti Te'o on third-and-goal from the 4, and Daniel threw a 2-yard TD pass to Dexter McCluster for a 14-7 lead.
San Diego tied it with an easy 4-yard scoring toss from Rivers to tight end Antonio Gates on the first play of the second quarter.
The Chiefs wouldn't go away, using an 11-play, 86-yard drive to take a 21-14 lead on a 2-yard run by Davis, who wasn't touched.
Daniel kept the drive going on a 29-yard scramble up the middle on third-and-5 from the Kansas City 19 and a 9-yard scramble for a first down at the Chargers 42. McCluster had a 12-yard reception and hurdled safety Jahleel Addae.