Making matters worse for Seattle, which dropped both games of the series against Texas and leads the Rangers by one-half game in the American League West, rookie right-handed reliever Shawn Kelley suffered a strained left oblique and was escorted off the field after throwing just three pitches.
He departed just three pitches into his 10th relief appearance.
Right-hander Denny Stark, who had pitched the previous two games, was summoned from the bullpen, took all the time he needed to get warm and retired the first two batters he faced.
Just when it appeared the Mariners were going to play their 13th one-run game of the season -- and fifth straight -- four singles, a walk and a grand slam sent most of the fans scurrying for the exits.
Stark said he couldn't remember the last time he pitched three consecutive days, but he said that was no excuse for what happened.
"I got two outs and couldn't find the third one for a while," he said. "They were able to find some open field, and it's just the way it goes sometimes. It was one of those days."
Catcher Jarrod Saltalamacchia settled the issue with his second career slam.
Considering how the first nine innings went, it was pretty remarkable that there was a 10th inning.
The Mariners went into the fifth inning without a hit for the fifth time this season, and this time it was a soft single into left-center by Wladimir Balentien that ended the no-no bid by Rangers right-hander Vicente Padilla.
Balentien also kept the game tied.
His strong throw from left field to catcher Rob Johnson in the eighth inning nailed Michael Young at home plate, keeping the game tied at 1.
It was a play that even Johnson had to shake his head in amazement.
"It was about 99 percent luck," Johnson said. "It was a good throw, but the ball took a weird bounce and just stuck in my mitt. It was like the ball went into my mitt at exactly the same time [Young] was hitting me. In all honesty, I didn't know I had the ball."
On offense, the closest the Mariners came to getting a hit during the first four innings off Padilla was Johnson's bunt-for-a-hit attempt leading off the third inning.
It was a good bunt, but Padilla hustled to the ball, which was rolling between the mound and third-base line, made a barehanded pickup, turned and made a strong throw to first base for the out.
Seattle got its first runner when Ichiro Suzuki walked to lead off the fourth inning. But he was quickly erased on a double play, the first of two turned by the Rangers.
Meanwhile, Mariners starter Erik Bedard had to work much harder to keep the Rangers away from home plate.
The lefty dodged a first-and-third, one-out jam in the first inning, pitched around Marlon Byrd's leadoff double in the second, and stranded a runner on second base in the fifth.
"I thought Bedard threw extremely well," manager Don Wakamatsu said. "It was a good outing by him, obviously, to keep that offense to one run. He made the one pitch on [Nelson] Cruz. It wasn't that bad of a pitch, but he had a good swing on it."
The pitch, a fastball, was supposed to be more inside than it was, and Cruz drilled it far over the fence in left field for his seventh home run of the season and the 48th for the Rangers, who lead the AL in that department.
Padilla, who entered the game with an 8.27 ERA, looked like Cy Young.
"It was one of those games where the offense needed to pick up the pitching and didn't do it," Wakamatsu said. "I thought we had an opportunity in the sixth with runners on first and third, but we didn't capitalize."
A hit batsman, a walk and an error by Texas second baseman Ian Kinsler snapped a scoreless deadlock and put the Mariners in position to have a much bigger inning. But Padilla induced Mike Sweeney to bounce into an inning-ending double play.
Bedard took the game through seven innings, giving a bullpen that had been used often during Sunday's 15-inning win against the Athletics a good chance to rest up.
"Padilla was outstanding, and we don't expect anything less from Bedard," Rangers manager Ron Washington said. "[Padilla] and Bedard were going back and forth, nobody would break. They would bend a little, but wouldn't break."
The Mariners (15-12) were swept in a series for the first time this season, and it hurt even more because it was against the team closest to them in the AL West.
"It means a lot, because it's a division foe," Washington said. "All we wanted to do was to come to Seattle and play good baseball, and I think we accomplished that."
Next up for the Mariners is a three-city, eight-game road trip to Kansas City (two games), Minnesota (three) and Arlington (three).