With the Mariners trailing 2-1, Kyle Seager led off the ninth with a single through the right side off Rays closer Fernando Rodney and Figgins came on to pinch-hit, putting a sacrifice bunt down the first-base line.
But Carlos Pena's throw to first sailed well past the bag, sending Seager to third and Figgins to second with nobody out.
"That's a play that Carlos makes 100 out of 100 times," Rays manager Joe Maddon said. "I don't know exactly what had happened, it was very routine."
Justin Smoak followed with a game-tying sacrifice fly to center, which also moved Figgins to third. After Miguel Olivo struck out, Thames came through with his heroic hit, a single that barely cleared the outstretched glove of second baseman Sean Rodriguez.
"I knew after that first fastball, he was going to come all splits," Thames said. "I faced him a lot over there with Toronto, so I knew he was going to throw it low and away, so I just sat in that zone and tried to hit through it. I got a piece of it, got enough of it to get it over Rodriguez."
"Good for him and good for us," Mariners manager Eric Wedge said. "That's arguably the best closer maybe in the game right now, with all the pitches that he throws, particularly that fastball and that changeup and the way he changes speeds and that arm action. He just did a good job of staying in the path of the baseball and got enough of it to get it over the infielder's head."
It didn't look like the Mariners would be anywhere near a post-game celebration, as the offense could not back up a solid effort by starter Kevin Millwood.
It took the Rays just two batters -- and an ill-advised dive attempt by left fielder Trayvon Robinson -- to get on the board in the first.
Desmond Jennings led the off the game with a single and scored a batter later when Robinson came up empty trying to grab a drive by B.J. Upton with a headfirst effort. Jennings scored on what ended up being an RBI triple and Upton touched home two batters later on a sacrifice fly by Evan Longoria.
But that was all Millwood would allow. He managed to retire the side in order just twice, but pitched well with runners on base, stranding men on second on four separate occasions.
The right-hander lasted seven innings, scattering eight hits, striking out a season-high eight and walking one. It was the sixth time this season that Millwood has received one run or less in a start.
"He had to work in multiple innings, but he's the best that I've ever seen in regard to working out of trouble and managing situations and executing pitches, especially when things get a little thick out there," Wedge said. "You saw him do it tonight. Just another great performance.
"We've struggled to get that guy wins. He's pitched well for us this year. The bottom line is to put your team in a chance to win ballgames, and that's what he does."
The Mariners got their first run in the second as Smoak hit a two-out double down the left-field line in his first at-bat since being recalled from Triple-A earlier on Tuesday. Olivo followed with an RBI double to left.
But that would be the extent of the Mariners' offensive output for the better part of the night, as Rays starter Matt Moore allowed just one runner to reach second base after the second inning. Moore struck out nine and walked one in seven innings of one-run ball.
Smoak and Dustin Ackley turned in impressive individual performances. Ackley went 3-for-4 out of the leadoff spot and Smoak went 1-for-2 with a walk and the game-tying RBI. Smoak came within feet of tying the game in the sixth, as his towering blast landed in Jennings' glove just shy of the wall in left-center field.
The offensive showing by Smoak was all the more impressive considering he was recalled from Triple-A Tacoma prior to the game. Smoak has played most of the season with the Mariners, but was hitting just .189 and was optioned to Tacoma on July 23.
"It always feels good to win, especially in that fashion," Smoak said of his return to the Majors. "I knew something was going to happen tonight where it was going to come up to me at some point in the game. It was good to come through right there."
Of course, Thames was warned the game was coming down to him, as well. Whether he believed Wells' prediction, that was up to him.