But it was more the name of his opponent than its defense that befuddled Smith.
"That's hard to get used to," said Smith, who grew up in San Diego. "I always know them as the 'San Diego Super Chargers.'"
The Chiefs (3-0) are becoming known as one of the NFL's top teams as Smith threw for two touchdowns before 25,386 at the StubHub Center.
Philip Rivers heaved three interceptions in the first half and the Chiefs took advantage.
"We were able to capitalize with touchdowns in the red zone and that was big," Smith said. "That changed the game."
Smith clicked with Tyreek Hill and Albert Wilson for first-quarter scores. Both of the touchdowns, as well as Cairo Santos' second-quarter field goal, came off turnovers by Rivers.
"I had a rough day," Rivers said. "And I made some terrible throws. It's a shame because the defense played great."
Kareem Hunt, who paced all rushers with 172 yards on 17 carries, had a 69-yard touchdown run late in the fourth quarter as the Chiefs were trying to run out the clock.
"He's doing a heck of a job," Kansas City head coach Andy Reid said. "It's his vision and his ability to stay patient. That's unique for a young guy."
The Chiefs (3-0) remain atop the AFC West and the Chargers (0-3) still seek their first win since moving from San Diego after 56 seasons. It was the Chargers' 14th loss in their last 15 games against a divisional foe.
No matter the locale, the Chargers haven't changed much.
"You might say we're the same old Chargers," first-year head coach Anthony Lynn said. "Well, right now we are. Until we prove differently, we are."
Smith was 16 of 21 for 155 yards.
Rivers, who has led or shared the NFL lead for most interceptions in two of the past three seasons, completed 20 of 40 passes for 237 yards.
L.A.'s Travis Benjamin paced all receivers with 105 yards on five catches.
Melvin Ingram had three of the Chargers' five sacks.
While the Chargers' offensive line was stout, it allowed a critical sack by linebacker Justin Houston on the last possession.
"I'm glad we're winning," Houston said. "I hope the guys appreciate the win because it's tough to come by. But to get to where we're going we got to be better."
The Chargers, who have lost 26 of their past 35 games, had to punt with about four minutes remaining. L.A.'s defense, which played well against the explosive Chiefs, was unable to stop Kansas City as Hunt got loose on his long scoring run to ice the win.
"That's not surprising because the defense was selling out and trying to make a big play," Smith said. "And he has big-play potential."
Rookie kicker Younghoe Koo, who hasn't come through late in both of the Chargers' losses, was good from 29 yards to pull L.A. within 17-10 just before halftime.
Rivers tossed his third interception of the half -- his career high is four in a game -- and the Chiefs cashed in again. Terrance Mitchell got his second pick and the Chiefs converted it into a 34-yard Santos field goal and a 17-7 cushion.
L.A. got back into the game toward the end of the first quarter thanks to Melvin Gordon's 11-yard scoring run around the right side. That sliced the Chiefs' advantage to 14-7.
Cornerback Marcus Peters intercepted Rivers on the Chargers' second possession when he took advantage of an ill-advised pass into heavy coverage. Rivers, who led the league with 21 interceptions last year, had two in his first four attempts.
Smith made it 14-0 when he clicked with Wilson for a 6-yard completion.
Rivers was sloppy with the football from the get-go. His second pass was intercepted by Mitchell and the Chiefs struck quickly. Four plays later, Smith found Hill for a 30-yard score on a crossing route for a 7-0 lead.
NOTES: Chiefs C Mitch Morse (foot) was unable to play. Zach Fulton, a former starting guard, slid over to fill in. ... Chargers RB Melvin Gordon (knee) left the game briefly before returning. ... Los Angeles CB Jason Verrett will undergo season-ending knee surgery. Verrett's attempt to return from last year's knee operation wasn't successful. ... Chargers RT Joe Barksdale (foot) was out of the lineup, replaced by Michael Schofield.