BEREA, Ohio—Inches from infamy, the only thing that stopped the Cleveland Browns from making unwanted history was another miss off the foot of a Buffalo kicker.

In jeopardy of becoming the first NFL team to blow leads of at least 13 points in three consecutive games, the Browns survived with a 29-27 win on Monday night when Bills kicker Rian Lindell pushed a 47-yard field goal to the right—a hauntingly familiar sight for Buffalo fans forever scarred by Scott Norwood’s notorious Super Bowl miss.

The Browns, whose season has been defined by hard luck and turmoil, finally ...

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