They made the most of both.
"We come out here in our first game and showcase to our home fans what we're about, and offensively we're out there flopping it around," said Gase, who was in no celebratory mood afterward. "It irritated me a little bit."
Tannehill threw for 319 yards and three touchdowns for Miami, and Landry caught seven of those passes for 120 yards.
Cody Parkey, who was signed Saturday after Patrick Murray was hurt the day before in practice, missed three field goals for Cleveland, including a 46-yarder as time expired in regulation. The Browns had a golden chance to win after Corey Lemonier stripped the ball from Tannehill and recovered the fumble himself with 20 seconds left.
Parkey went wide left, some Dolphins fans who were leaving turned around in the stairwells, and to overtime they went.
"I know everybody will say it came down to the field goals, but I'm not going to put that kind of pressure on Cody," Browns coach Hue Jackson said. "Cody just got off a plane with us and I don't know him as well as I know this chair right now."
Terrelle Pryor became the first Browns player since 1977 to have multiple receptions, rushes and passes in the same game. The former Ohio State quarterback, now primarily a receiver, started taking some snaps in the game's second series and finished with eight catches for 144 yards - along with 35 passing yards and 25 rushing yards. Pryor even played safety on the last play of the first half.
"Dynamic athlete," Miami defensive tackle Ndamukong Suh said. "Whether he's playing quarterback or wide receiver he's obviously effective."
Cleveland's first offensive touchdown in its last 16 series came with 10:12 left, when Pryor scored on a 3-yard run. The two-point conversion got the Browns within 24-21, and Parkey's 38-yard field goal later in the fourth pulled Cleveland into a tie.
And in OT, Ajayi - who didn't even fly with the team to Seattle for its season opener - capped it with a run around the left side.
"I'm always happy to get a win. It was ugly, we didn't play well at times today, but we stuck together and found a way," Tannehill said.
Briean Boddy-Calhoun was inactive in Week 1 and Week 2 for Cleveland. He made his debut one to remember, becoming the first player in franchise history to run back an interception for a score in his first NFL game.
Cleveland won the coin toss prior to overtime and let Miami have the ball, even though a Dolphin touchdown on that possession would have ended the game. Miami wound up punting. "The way we were playing offensively, it was probably a good idea," Gase said.
Patriots coach Bill Belichick offered a memorable "We're on to Cincinnati" series of quotes in October 2014, not wanting to answer questions about Tom Brady after a bad loss to Kansas City. Gase, whose club goes to Cincinnati on Thursday, channeled some Belichick on Sunday. "We're moving on to Cincinnati," Gase said.
Dolphins C Mike Pouncey (hip) missed a third straight game, and his replacement - Anthony Steen - left with an ankle injury 15 seconds into the fourth quarter, so Miami turned to third-stringer Kraig Urbik. The Dolphins also lost LB Jelani Jenkins (quad), LB Koa Misi (neck) and TE Jordan Cameron (assessment for concussion).
Copyright 2016 by The Associated Press