"If I hit that ball one-sixteenth of an inch lower, that's probably a home run," Damon said. "That's how close it was."
Detroit closer Jose Valverde gave up two runs in the ninth but avoided a total collapse by retiring Damon on a line drive.
"That game wasn't lost in the ninth," Rays manager Joe Maddon said. "It was lost early on when we didn't take advantage of those scoring opportunities early in the game."
Charlie Furbush had something to do with that.
Furbush (1-0) pitched 3 2-3 scoreless innings of relief, suddenly entering the game for his major league debut after Tigers starter Phil Coke injured his right ankle.
"I was trying to hold back some smiles there, that's for sure," Furbush said. "It was great to be out there."
Jeremy Hellickson (5-3) allowed two runs and four hits in 6 1-3 innings. He had a shot to be the first Tampa Bay rookie to win five straight starts, but his light-hitting teammates weren't much help.
"Helly pitched a great game, but we didn't get the runs we needed," Maddon said.
The Tigers, meanwhile, scored more than three runs for the first time in nine games. In fact, they did that with two outs in the eighth inning alone after leading by only a run.
Detroit has won two straight after losing five in a row.
Tampa Bay has lost five of seven after building a season-high, three-game lead over the New York Yankees in the AL East.
After the start of the series opener was delayed 27 minutes by rain, Evan Longoria's sacrifice fly gave the Rays a 1-0 lead in the fourth inning. Andy Dirks made it 1-all in the fifth with his first homer in the majors.
Coke started strong, needing just nine pitches to retire the side in the first and keeping the Rays off the basepaths until B.J. Upton drew a leadoff walk in the fourth. Coke's outing ended in that inning though, when Ben Zobrist laid down a perfect bunt on the left side of the infield and the pitcher said he bruised his right ankle while trying to field it.
Rays shortstop Elliot Johnson left in the fifth with a sore left knee after being thrown out attempting to steal third. Johnson was limping badly after the game.
The Tigers went ahead in the sixth when Brennan Boesch hit a two-out double and scored — getting around a throw up the third-base line from Matt Joyce in right — on Cabrera's tiebreaking single.
Hellickson was removed with one out in the seventh after making 100 pitches. J.P. Howell made the move pay off, getting Alex Avila to ground into an inning-ending double play that kept Tampa Bay within a run. But the Rays are struggling on offense — they have scored three runs or fewer in eight of the last 11 games.
Howell and Juan Cruz combined to give up four runs in the eighth.
NOTES: Tampa Bay and the 2010 Minnesota Twins are the only teams in major league history to avoid having more than one error in their first 48 games, according to statistics provided by the Rays from the Elias Sports Bureau. ... Tampa Bay plans to stick with RHP Andy Sonnanstine in the series finale Wednesday despite his 0-1 record and 6.08 ERA in three starts this year. ... Rays OF Justin Ruggiano was taken out of the lineup with a stomach ailment.