Tannehill began his second season as Miami's starting quarterback with 272 aerial yards and a touchdown as the Dolphins (1-0) logged a victory after going 7-9 last season.
Tannehill's favorite target was Brian Hartline, who made nine catches for 114 yards, including a go-ahead 34-yard TD grab in the third quarter.
Miami's defense harassed Browns quarterback Brandon Weeden, not only with the six sacks but also with three interceptions, holding Cleveland to three points in the second half.
Weeden finished 26-of-53 through the air for 289 yards with a touchdown as the Browns (0-1) lost in the debut of head Coach Rob Chudzinski.
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