Garrard was scheduled to start after being listed first on the depth chart, but his agent confirmed Friday he's slated to have knee surgery. His absence is likely to knock him out of the three-way battle for the starting quarterback job he was waging with Tannehill and Matt Moore, who started the last 12 games last season for Miami.
Dolphins starting linebacker Kevin Burnett also missed the game despite taking part in warm-ups. Backup offensive lineman Nate Garner was helped off the field in the fourth quarter after sustaining an ankle injury.
Tannehill, taken eighth overall in the 2012 draft, is the Dolphins' quarterback of the future, but he's hoping to convince his coaches to make him a starter right away.
He made a pretty argument for his case on Friday night.
Before his TD pass, a strike down the middle, Tannehill had a touchdown pass to wide receiver Roberto Wallace late in the second quarter overturned by instant replay. Two plays later, Tannehill missed Clay near the sideline on a fourth-and-goal from the 3-yard line.
He was 8 for 9 on his touchdown drive, the highlight a beautiful touch pass to Wallace over a linebacker that was good for 19 yards on a third-and-11. The only incompletion on the drive was a pass that was batted down at the line of scrimmage.
Tannehill, who finished the game with a 106.6 passer rating, entered with 3:16 left in the second quarter to the applause of a sparse crowd still sitting despite a driving rain. His first pass, on a third-and-6, was thrown behind wide receiver Julius Pruitt and led to a three-and-out.
Matt Moore got the start in Garrard's place and completed 7 of 12 passes for 79 yards with one interception for a rating of 43.4.
Moore, though, was the victim of some bad luck. He produced three first downs on his first drive, only to see Chad Johnson let a pass go through his hands on third-and-3 from the Tampa Bay 33. It was the only pass thrown in Johnson's direction.
The Dolphins' second-round pick of the 2012 draft, tackle Jonathan Martin, also got extended playing time but had an up-and-down performance. Martin started at right tackle and played into the third quarter, long after the other starting offensive linemen had left the game. Martin held up well in pass protection but also was flagged for two false starts.
For Tampa Bay, the game was a good start under new head coach Greg Schiano.
The Bucs looked sharp offensively at the start of the game, scoring touchdowns on their first two possessions.
Starting quarterback Josh Freeman left the game after playing only one series, completing 4 of 5 passes for 41 yards. LeGarrette Blount finished off the drive with a 1-yard touchdown plunge on fourth-and-goal.
Bucs first-round pick Doug Martin scored on a 2-yard run on Tampa Bay's next drive and finished with 21 yards on seven carries.
Tampa Bay's third-quarter field goal was set up by a 74-yard kickoff return by rookie seventh-round pick Michael Smith, a running back from Utah State.
Indianapolis Colts quarterback Andrew Luck will not play Sunday against the Jacksonville Jaguars because of a right shoulder injury, a team source told ESPN's Chris Mortensen.
Texans running back Arian Foster, barring a pregame setback, will make his 2015 debut against the Falcons, a source told ESPN NFL Insider Adam Schefter on Sunday.
Eagles running back DeMarco Murray, who has been hampered by a hamstring injury, is expected to play against the Redskins, a source told ESPN NFL Insider Adam Schefter.
Jets receiver Eric Decker, who was listed as questionable with a knee injury, will be active for Sunday's game against the Dolphins in London.
Quarterback Jay Cutler will test his injured hamstring prior to Sunday's game, and the Bears are optimistic he'll play against Oakland, a source told ESPN NFL Insider Adam Schefter.
Drew Brees told ESPN NFL Insider Ed Werder that he believes his passing shoulder is healthy and he is capable of making every throw necessary when the Saints host the Cowboys on Sunday night.