Ryan Mathews ran for 98 yards and a pair of 17 victory over the struggling Chiefs.
"For it to end the way it did with that interception, that's all on me," a disappointed Cassel said. "It hurts."
Cassel threw for 176 yards and two touchdowns. With Pro Bowl running back Jamaal Charles out for the season, the Chiefs (0-3) turned to Thomas Jones, who gained just 31 yards on 14 carries. Dexter McCluster was more effective, gaining 45 yards on nine carries.
Philip Rivers completed 24-of-38 passes for 266 yards and a pair of interceptions for San Diego, which won the division from 2006-09 before Kansas City went 10-6 to grab the title last season.
The Chargers faced double digit deficits at the half in each of their first two games, but paced the faltering Chiefs, 10-0, through two quarters on Sunday.
Kansas City's sputtering offense received a jolt in the form of Javier Arenas' 37-yard punt return early in the third quarter. Cassel found Dwayne Bowe at the San Diego four-yard line for a 23-yard strike before connecting with the receiver in the end zone to make it a 10-7 game.
The Chargers responded immediately. Rivers hit Randy McMichael for a 26-yard catch-and-run on the team's next play from scrimmage. Later in the drive, Mathews' four-yard touchdown plunge put San Diego on top 17-7.
"The linemen are doing a great job opening up [holes] and I've got to find them and run through them," said Mathews. "It's just me being more comfortable and the game is slowing down."
The Chiefs' Ryan Succop hit a 33-yard field goal at the start of the fourth quarter, but Nick Novak answered with a 41-yarder on the Chargers' ensuing drive, resulting in a 20-10 margin.
Kansas City received the ball with 8:03 remaining and Cassel converted two third-and-longs to Bowe during a nine-play, 80-yard touchdown drive. He hit Steve Breaston for a 43-yard strike down the sideline to the San Diego one- yard line and found Leonard Pope in the back of the end zone to pull the Chiefs within a field goal.
With 1:26 remaining, Rivers was stopped on a 4th-and-1 sneak, but Cassel was intercepted two plays later, sealing the Chiefs' fate.
Rivers was intercepted twice in the first half, but the Chiefs, without Charles, were unable to capitalize.
Kendrick Lewis picked off Rivers early in the first quarter. The Chiefs took over at the San Diego 20-yard line, but Succop's 38-yard field goal attempt sailed wide right.
The Chargers responded with a methodical, 15-play, 76-yard drive, which was capped by Mathews' short touchdown run, to take a 7-0 lead early in the second.
Midway through the second quarter, Brandon Flowers picked off Rivers near midfield, but the Chiefs went three-and-out.
Novak tacked on a 35-yard field goal towards the end of the quarter.
Rivers improved to 34-8 as a home starter. His streak of consecutive 300-yard passing games ended at three...Bowe caught four passes for 67 yards...Charles tore the ACL in his left knee during Sunday's 48-3 loss at Detroit. He was placed on injured reserve Wednesday.