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The hosts last week became the first side to be mathematically ruled out of this season's playoff race with their seventh consecutive defeat, and they were left bemoaning their luck again after seeing Travis Coons's field goal blocked on the opening drive of the game.
A fumble from Glenn Winston handed the 49ers a chance to get on the board, but their offense failed to fire on all cylinders throughout the first half and they were unable to take advantage.
In contrast, Johnny Manziel was enjoying some success having been restored to the Cleveland team, and he led his side into kicking range in the second quarter, allowing Coons to this time split the posts.
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A Phil Dawson field goal finally got the visitors on the board and Manziel threw an interception in the closing stages of the half to give them a platform to go in level, but once again they could not make the most of it.
Cleveland, meanwhile, were impressing on both sides of the ball, ending the game with nine sacks on Blaine Gabbert and extending their lead to 14 in the third quarter when Manziel marked his return with a two-yard pass to Gary Barnidge.
Crowell added his second rushing touchdown of the match to take the game further away from the 49ers' reach, and despite a late reply from Jerome Simpson, who combined with Gabbert for a six-yard score, Cleveland ran out fairly comfortable winners.
A first win in eight takes the already-eliminated Browns to 3-10 for the season, while the 49ers' own playoff hopes look increasingly bleak as they drop to 4-9.