Edwards-Helaire -- the No. 32 overall pick in the 2020 NFL Draft -- averaged 6.1 yards per carry in the 26-17 win on Monday at New Era Field in Orchard Park, N.Y. Chiefs quarterback Patrick Mahomes was also sharp as he completed 21 of 26 passes for 225 yards and two scores.
"Clyde was running well and the offensive line was blocking well," Mahomes said. "I just want to win. I don't care how it is done; pass, run or defense. Whatever it is. We found a way to do that."
The Chiefs outgained the Bills 466 to 206 in total yards and held a 37:45 to 22:15 edge in time of possession as they used Edwards-Helaire's success to drain time off the clock.
Kansas City players said they used last week's loss to the Las Vegas Raiders as motivation for the victory.
"It was our mindset," Edwards-Helaire said. "Everybody knows: When it comes to football it starts up front. The offensive line did its job and made things easier for me."
Tyler Bass made a 48-yard field goal to give the Bills a 3-0 lead with 5:47 remaining in the first quarter of Sunday's game. The Chiefs responded with a five-play, 75-yard touchdown drive. Mahomes connected with tight end Travis Kelce on an 11-yard touchdown toss to give the Chiefs a 7-3 lead.
Bills quarterback Josh Allen responded with a four-yard touchdown pass to Stefon Diggs on the next drive, but the Chiefs punched right back with another Mahomes-to-Kelce touchdown connection 5:01 before halftime.
Bass then missed wide right on a 52-yard field goal attempt and the Chiefs held a 13-10 lead at the break.
The Chiefs and Bills each punted to start the second half before Kansas City got the ball back into the end zone with a 13-play, 87 yard drive. Chiefs running back Darrel Williams ended the drive with a 13-yard touchdown run.
Chiefs kicker Harrison Butker made a 37-yard field goal with 9:11 remaining. Allen then hooked up with Cole Beasley on an eight-yard touchdown throw on the next possession to cut the Chiefs lead to 23-17.
Butker made another field goal on the next drive to give the Chiefs a nine-point advantage. Allen threw a game-ending interception on the Bills final possession.
"We weren't good enough," said Allen, who completed 14 of 27 passes for 122 yards, two scores and one interception in the loss.
"I was not good enough. I have to do a better job. This team can't afford to have me play poorly. I was not as accurate with the ball as I should have been. We turned it on a little too late and 16 or 17 points is not going to cut it in this game."
The Bills (4-2) face the New York Jets at 1 p.m. EDT on Sunday at MetLife Stadium in East Rutherford, N.J. The Chiefs (5-1) battle the Denver Broncos at 4:25 p.m. EDT on Sunday at Empower Field at Mile High in Denver.