"We got the monkey off our back," Fitzpatrick said. "We always felt confident. This is a new year, a new team, but it was a good team win on the road. These are the most satisfying wins."
As the final seconds ticked off, some of Buffalo's players celebrated with hundreds of Bills fans who made the short drive over from Western New York.
Before he went out, Spiller, who came in leading the league with 292 rushing yards, scored on a 32-yard screen pass from Fitzpatrick, who also threw a 9-yard touchdown to T.J. Graham in the first quarter and hooked up with Stevie Johnson from 9 in the fourth to close the scoring.
"I don't believe it's long, long-term," Gailey said. "If he missed a week that's long for me. He's going to be out for sure this week and then we'll see."
Spiller will undergo further testing Monday. He was not available for interviews.
Cleveland has lost nine straight dating to last season, and one of the league's youngest teams was not able to build off a solid performance last week in Cincinnati.
"We just didn't get it done," said coach Pat Shurmur, who dropped to 4-15 in two seasons. "There are no magical answers. We just didn't get it done."
Fitzpatrick got great protection from an offensive line that has only allowed one sack this season. He passed around some compliments afterward, crediting his teammates for stepping up without Spiller.
"We knew we had to put our foot on the gas again and when we did, the offensive line was revved up and ready to go," he said. "It was a heck of a job by Tashard. He got some really tough yards for us."
"We wanted to stop Richardson," Gailey said. "We talked about it and made a big deal about it. We did not want to let him get out. We wanted them to throw the football. It worked kind of like we thought it would."
Fitzpatrick later led a 10-play, 68-ard drive, capping it by rifling his TD pass over the middle to Johnson, who got a step on cornerback Dimitri Patterson.
Spiller was injured in the first quarter when he was tackled after a long gain on a pass play.
He was placed on a cart and driven to the locker room for further evaluation and treatment.
At that point, Buffalo's chances of ending its road slide seemed bleak.
"It was tough to lose him," said Johnson, who had seven catches for 61 yards. "We have guys who can fill the void."
NOTES: Bills DE Mario Williams recorded his first sack with Buffalo, which signed him to a $100 million free agent contract in March. ... With his touchdown reception, Spiller has scored a TD in six consecutive games, the longest streak by a Buffalo player since Hall of Famer Thurman Thomas' six-game streak in 1990. ... Browns WR Mohamed Massaquoi injured his hamstring in the second half and did not return. ... It's a short work week for the Browns, who will play at Baltimore on Thursday.
Copyright 2012 by The Associated Press