The 26-year-old quarterback was dominant from the outset, finding the end zone three times in the first half before adding two more late on.
The Chiefs defence also did well to hold Arizona quarterback Kyler Murray to under 200 yards as the 2020 NFL champions began their 2022 campaign in imposing fashion.
Tom Brady also began his 22nd season in style, leading the Tampa Bay Buccaneers to a 19-3 victory over the Dallas Cowboys.
After a slow start from both teams, Brady finally found the end zone with a five-yard pass to Mike Evans.
Four field goals sealed the result for Tampa as Cowboys quarterback Dak Prescott was forced from the game with a hand injury.
A dominant defensive display handed the Miami Dolphins a 13-point win against AFC East rival the New England Patriots.
The defence came away with a touchdown, an interception and a forced fumble while keeping the Patriots' offence quiet for all but one drive.
Missed opportunities for Green Bay summed up the story of the Packers' 23-7 loss to the Minnesota Vikings.
Rookie wide receiver Christian Watson dropped a 75-yard touchdown pass on the opening play of the game as quarterback Aaron Rodgers gave up a crucial interception and fumble en route to a 16-point defeat.
Carolina Panthers quarterback Baker Mayfield fell just short against his former team, going down 26-24 to the Cleveland Browns.
The New Orleans Saints came from behind to beat the Atlanta Falcons 27-6.
The Bears overcame the San Francisco 49ers by nine points in torrential conditions in Chicago.
The Indianapolis Colts were forced to settle for a 20-20 tie with the Houston Texans after Rodrigo Blankenship missed a 42-yard field goal in overtime.
The Pittsburgh Steelers, Philadelphia Eagles, Baltimore Ravens, Washington Commanders, New York Giants and Los Angeles Chargers rounded out Sunday's week one victors.