The loss kept the Rangers from reaching .500 for the first time since April 11.
Miguel Cairo's two-out single in the 12th drove in the winning run after each team had squandered chances.
Rangers manager Ron Washington said: "We were in that game all day. In the seventh, eighth, ninth, 11th and 12th we had an opportunity to put it away. Today we just didn't get a hit when we needed one."
In fact, after Josh Hamilton's sacrifice fly tied the score in the eighth inning, Texas managed just two singles -- both by David Murphy, who went 4-for-5.
Over the last six innings, the Rangers left seven runners on base, four in scoring position. Washington's strategic moves didn't pan out either. Pinch-hitter Marlon Byrd grounded into a double play with the bases loaded to end the seventh, and Chris Shelton's sacrifice bunt attempt in the ninth also turned into a double play.
Cairo's hit against Franklyn German (1-2), the Rangers' sixth pitcher, drove in Wladimir Balentien, who had led off the inning with a single. He advanced to second base on Yuniesky Betancourt's sacrifice, then to third on Ichiro Suzuki's long fly ball.
The Rangers had taken a 2-0 lead in the first inning, and didn't trail until the seventh.
Leading off that inning, Seattle's Jose Lopez reached second base on third baseman Ramon Vazquez's throwing error. Hamilton then started in on Jeff Clement's fly ball, which sailed over the center fielder's head for a triple.
"Vazquez makes a good play there and throws the ball away; [Hamilton] misreads the ball off the bat -- all that did was give them the opportunity to win," Washington said. "Physical mistakes are part of the game. We got back in it, so I don't feel like we gave the game away."
Rangers starter Scott Feldman retired two batters to keep Clement on third base, but Yuniesky Betancourt doubled off the scoreboard in left field to give Seattle its lead.
"The one breaking ball, when Betancourt got the double, was the only pitch [of 99] I was really upset with," Feldman said.
He allowed one earned run and six hits in a career-high seven innings. He said his two-seam fastball was responsible for most of his 15 ground-ball outs.
Seattle's Carlos Silva held the Rangers to five hits -- curiously, all doubles -- in 6 1/3 innings. Neither starter walked a batter.
Feldman arrived in the Majors in 2005 as a sidearm relief pitcher. This spring, Texas converted him to a starter, throwing from a high-three-quarters angle.
"Feldman did an excellent job, he really did," Washington said. "I'm surprised at how he's adjusting and pitching well, with the arm angle and all. He's coming along quicker than we thought he would. It's too bad he didn't get the win."
The Rangers' first-inning runs came with the help of what appeared to be shaky fielding by Balentien.
With one out, Frank Catalanotto doubled into the right-field corner. Michael Young followed with a line drive toward right-center field. Balentien ran after the ball, but it sailed over his backhand attempt. After he retrieved the ball, he threw to second base, where Young was safe with a double. A relay throw home barely missed tagging out a sliding Catalanotto.
Murphy's two-out double into the right-field corner drove in Young.
Feldman allowed only one of the Mariners' first 12 batters to reach base, but with two out in the fourth inning, Raul Ibanez singled and scored on Lopez's double.