Fitzpatrick connected on 17-of-26 passes and finished with 208 yards for Buffalo (1-0), which is coming off a 4-12 campaign. Last season, the Bills began the Chan Gailey era with eight consecutive defeats.
Scott Chandler made five catches for 63 yards and two touchdowns.
Matt Cassel completed 22-of-36 passes for 119 yards with one touchdown and one interception for the Chiefs (0-1), who went 10-6 last season -- a six-win improvement, the largest in team history -- and captured the AFC West title for the first time since 2003.
"It doesn't need a lot of description. We did the things that, if you do them, you're going to get beat," said Kansas City head coach Todd Haley. "I'm taking 100 perecent responsibility for our team not being ready to go. You could point the finger right at Todd Haley. I'm taking 100 percent responsibility. That being said, I believe in those guys in that room over there. I really do."
It was not an ideal way to start the season as Kansas City's Dexter McCluster fumbled the game's opening kickoff. The turnover led to a four-yard touchdown pass from Fitzpatrick to Chandler.
"I thought we did some very good things," Gailey said. "It started on the opening kickoff. That set the tempo and it was a good football game for our football team."
Buffalo extended its lead to 14-0 when Stevie Johnson leaped up and pulled down a 27-yard touchdown catch just inside the end zone with 55 seconds remaining in the first quarter.
The Chiefs appeared to have scored on their next series, but Leonard Pope's 19-yard TD reception was overturned after a video review determined the tight end failed to maintain possession. Buffalo's Spencer Johnson tripped up Cassel on third down, and the sack set up a 49-yard field goal attempt that Ryan Succop missed wide right.
Rian Lindell's 250th career field goal -- a 29-yarder -- put the Bills ahead 17-0 before a Jamaal Charles fumble deep in Kansas City territory set up a 38- yard conversion by the Buffalo kicker.
Kansas City then went on an 11-play, 81-yard drive, and Charles hauled in a six-yard pass from Cassel to put the Chiefs on the board with 1:46 left in the first half.
Following the break, Fitzpatrick found Chandler for an 11-yard TD and connected with Donald Jones on a four-yard score to make it 34-7 in the third quarter.
C.J. Spiller tacked on a nine-yard TD run in the final stanza.
Chandler is the first Buffalo tight end with two touchdowns in a road game since Pete Metzelaars on September 13, 1992 at San Francisco...Jackson became the first Bills running back to rush for 100 yards in the season opener since Willis McGahee in 2005 versus Houston...Stevie Johnson and teammate David Nelson both had 66 yards on four receptions...Charles gained 56 yards on 10 carries...Kansas City was 7-1 at home last season...The Bills visited Kansas City for the fourth consecutive year.