The Mariners managed just four runs in 32 innings against the Rangers, and the sweep drops them to 11-14, last place in the American League West and two games behind first-place Texas (13-12).
The series also marks the first time the Rangers have swept the Mariners at Safeco Field.
Seattle looked in control with Fister on the mound, taking a slim lead on an RBI single from Franklin Gutierrez in the fourth. Fister carried a perfect game through 5 1/3 innings. After allowing just three hits and zero walks in eight innings, Fister was pulled for closer David Aardsma, who entered the game as the AL saves leader with eight.
But Aardsma issued a nine-pitch walk to Elvis Andrus, who stole second base, and two batters later David Murphy laced a game-tying RBI single. Andrus drew the walk after fouling off two pitches on a 2-2 count.
"I knew he was going to be aggressive with his fastball," Andrus said. "I was just trying to hit it up the middle or the other way. After I got two strikes, I just tried to battle. I knew he was going to throw a lot of fastballs."
That was only Aardsma's second blown save since Aug. 20, 2009, and both of those slip-ups have come during games Fister has started. On April 24, Fister held the White Sox to two runs in eight innings, but Aardsma gave up two home runs in the ninth, and Seattle lost, 5-4.
"There is no room for error," Aardsma said. "When you give up a couple of hits and a run, that's better than giving up a leadoff walk to a fast guy. You just can't do it. You can't let that happen. You are pretty much handing them a run."
After Brandon League pitched a scoreless 10th inning, Mark Lowe came in for Seattle in the 11th.
Julio Borbon singled and got to second on a passed ball, then moved to third on Andrus' bunt single and scored on a sacrifice fly from Murphy. Andrus would later score on another passed ball.
Catcher Rob Johnson took the blame for both passed balls, simply saying, "I missed them." It was an especially frustrating day for Johnson, who went 0-for-3 at the plate and watched two well-hit balls turned to outs by Borbon in center field.
After Gutierrez drove in Chone Figgins in the fourth, Seattle had the bases loaded with one out and a chance to add more. Eric Byrnes struck out, and Johnson hit a deep line drive to center field that looked like it would widen the lead. But Borbon snagged it on the run near the warning track to end the inning.
"That's a three-run double in most ballparks," Mariners hitting coach Alan Cockrell said. "Today, I really feel like we had great at-bats, we just didn't catch a break."
The Mariners were 1-for-6 with runners in scoring position, an area where they were 4-for-29 on the series. In the eighth, Figgins and Gutierrez reached base with zero outs, but Texas first baseman Ryan Garko -- who was cut by the Mariners in Spring Training -- made a jumping catch and threw to second base, turning a potential RBI double into a double play.
It was another case of the Mariners not getting the hits to match solid pitching and defense. Fister carried a perfect game into the sixth inning, helped along by Seattle's reliable fielding. Right fielder Ichiro Suzuki made the play of the day by robbing Rangers first baseman Justin Smoak of a home run for the first out of the sixth to preserve the lead and the perfect game.
The latter slipped away one batter later, when catcher Max Ramirez lined a single to left field. Fister watched the win evaporate from the dugout, where he was one of the first to console Aardsma after the blown save.
"We still have the utmost confidence in him," Fister said. "That's why he's our closer, and that's why we have him here. Unfortunately, everybody has a bad day once in a while, and it just so happened that today we didn't come out on top."
It was Fister's fourth straight outing of at least seven innings with two or fewer earned runs allowed. The last Seattle pitcher to accomplish that was Felix Hernandez last year. The club record is seven, held by Randy Johnson.
The Mariners will host the Rays in a three-game series starting Tuesday before closing out the homestand with the Angels next weekend.