ORCHARD PARK, N.Y. -- The Buffalo Bills expected to beat the Cleveland Browns on Sunday. One player even guaranteed victory.

The LeSean McCoy-led ground game made sure the Bills backed up their boasts.

"We talked about going out there and dominating. It's a game we should win," McCoy said. "Well let's play like it."

McCoy had 153 of the Bills' 275 rushing yards and scored two touchdowns as the Bills beat the Browns 33-13 at New Era Field to snap a two-game losing streak and keep their slim playoff hopes alive.

The Browns lost their 17th straight game dating back to last season and became the fourth team in NFL history to start 0-14.

"You're nervous when you play an opponent like that because you definitely don't want to be the team that gets beat by them," Bills coach Rex Ryan said.

Embattled quarterback Tyrod Taylor was 17 of 24 passing for 174 yards for the Bills (7-7). Tight end Charles Clay had his best game of the season with seven receptions for 72 yards and touchdown.

Taylor also ran for 49 yards and Mike Gillislee gained 37 yards to bolster the NFL's top-ranked rushing offense. Gillislee had one of the three rushing touchdowns, bringing Buffalo's season total to 27, a franchise record.

McCoy's rushing total was his highest in two seasons with the Bills and put him over 1,000 yards for the fifth time in his career.

"The game ball today goes to the guys up front," McCoy said. "Numbers-wise this was my best game as a Bill, but I don't think it was my best performance as a Bill. It was a lot of easy yards."

Yards were harder to come by for the Browns, who were out-gained 451-269.

Robert Griffin III couldn't ignite the Browns' offense in his second start after missing 11 games with a broken bone in his left shoulder. Griffin completed 17 of 28 passes for 196 yards and was the Browns' leading rusher with 48 yards and a touchdown.

"It's been tough these past two weeks," Griffin said. "But I can tell you one thing, we're not going to quit. We're going to keep working hard and we're going to find a way. We have to find a way, no matter what. Even if we've got to turn it into a backyard brawl, backyard football, we're going to find a way to get a win, and that's what everybody in that locker room's focus is.

Coach Hue Jackson remained upbeat about the Browns' chance to win one of their final two games and avoid become the second team in NFL history to go 0-16.

"This wasn't my dream by any stretch of the imagination, but I'm not running from this," Jackson said. "These players mean too much to me, the people here mean too much to me so I've said a long time ago, we're going to fix this and we have to. We have nowhere to go but up, and we've got a lot of work."

Buffalo put the game away by scoring on three straight possessions in the second half.

McCoy found the end zone on a 3-yard run midway through the third quarter and an 8-yard run early in the fourth to give the Bills a 30-13 lead. Dan Carpenter added a 34-yard field goal later in the fourth.

Griffin brought the Browns within a touchdown on their first drive of the second half when he lunged across the goal line at the end of an 18-yard scramble.

Taylor led a 91-yard drive that spanned half of the second quarter and connected with Charles Clay for a 19-yard touchdown that gave the Bills a 17-3 lead heading into halftime.

The Bills rushed for 97 yards on their first two drives and went ahead 10-3 on Gillislee's 3-yard run at the end of the first quarter.

Both teams settled for a field goal after reaching first-and-goal at the 5 in the first quarter. McCoy ran for 44 yards on his first two carries to set up Carpenter's 21-yard kick. Cody Parkey tied the game with a 35-yard field goal. Parkey also hit from 40 yards out in the third quarter.

NOTES: Buffalo won its 400th regular season game ... The Browns have not led at any point in their last four losses. ... Buffalo QB Tyrod Taylor moved past Jim Kelly for the second-most rushing yards by a quarterback in franchise history on a 28-yard run that led to McCoy's first touchdown. Taylor has rushed for 1,088 yards in 28 games with the Bills. ... K Dan Carpenter missed his fifth extra point of the season. ... Bills LT Cordy Glenn (back) did not play.