The defeat ended a 10-game homestand with a 4-6 mark for Tampa Bay, which dropped two of three to Seattle.
"We had every opportunity the last two days, pitching was really good enough to permit us to win these games," Rays manager Joe Maddon said. "The offense has been challenged lately. Obviously we just have to do better there, we have to figure it out to score more runs. ... It could've, should've been better."
Moore pitched well, despite giving up a run in each of the first two innings, retiring the final 17 batters he faced. The eight-inning outing was the longest of his short career. He finished with seven strikeouts and allowed just five hits without issuing a walk.
"That was really kind of the mindset ... attack and make them beat me with base hits and not walks and working counts," Moore said. "It felt like it was a tie game the whole game with them. We went back and forth with quick innings, it was a fun pace to pitch at."
In the first, Ichiro Suzuki reached base on a bunt attempt that resulted in Casper Wells being thrown out a third, then stole second and third base before a double by Jesus Montero brought in the first run. Seattle scored again in the second after Brendan Ryan doubled home Michael Saunders with two outs.
After a one-out single in the third, Moore was perfect for the rest of his outing.
"I think I probably started locating my fastball better," Moore said. "I saw some not-so-good swings on some fastballs tonight that were just better located. I think it just had to do with throwing more strikes with my fastball."
The only run support he received came in the bottom of the first. Ben Zobrist knocked a two-out double and Matt Joyce hit an RBI single to even the score before Seattle took the lead again in the second.
"It's the same old story, we've got to find a way to score runs," Joyce said about the lack of scoring. "I don't know, I really don't have an answer. I think everybody's kind of in the same mindset where we're just kind of waiting for something to come along or hoping some hits come or something. We've got to find a way to score runs, however."
The Rays had a chance to score in the eighth when a fielding error helped Desmond Jennings reach base. After a pair of groundouts got him over to third, Upton popped out to end the inning.
"He was spotting up, and he was pitching guys tough," B.J. Upton said of Mariners starter Blake Beavan. "We haven't really seen him, so hats off to him. He threw a really good game."
Joyce hit a two-out double in the bottom of the ninth, and Jeff Keppinger drew a walk from closer Tom Wilhelmsen for the Rays last offensive threat. Maddon sent in Hideki Matsui as a pinch-hitter, but he popped out, ending the game.
Beavan also threw eight innings, allowing the one run against him on four hits and no walks with five strikeouts. He had previously allowed 22 runs in his last four starts combined.
"He did a great job with his fastball, moved it around, in and out, up and down," Seattle manager Eric Wedge said of Beavan. "But his secondary stuff was big for him. He did a good job mixing his pitches, moving the ball around, was aggressive and really controlled the ballgame."
Tampa Bay only had four at-bats with runners in scoring position on Sunday, converting one chance for a run. In the series, the team was just 3-for-25 with runners in scoring position and 17-for-93 on the homestand.
"Of course Luke [Scott] is hurt and all this other stuff, but nevertheless, we should be able to score more than two runs," Maddon said. "That's something we have to figure out somehow. There's no excuses, there's absolutely zero excuses to not do better."
Moore's long outing was a welcome sight to a tired bullpen for the Rays, which threw 36 2/3 innings coming into Sunday's matchup on the homestand, including 13 1/3 against the Mariners. Kyle Farnsworth was the only arm used out of the bullpen and threw a scoreless inning.