Moore's outing had an inauspicious beginning when he hit Pirates leadoff batter Starling Marte, then walked Jordy Mercer.
Russell Martin singled home Marte before Brandon Guyer missed Pedro Alvarez's drive to right field, allowing Mercer to score. Gaby Sanchez added a two-run double while Jose Tabata and Marte added RBI singles to give the Pirates a 6-0 cushion.
Sam Runion took over for Moore after Marte's single and retired Mercer on a groundout to end the inning.
Moore allowed six runs -- four earned -- on five hits and a walk. He threw 41 pitches, 25 for for strikes.
"We're in a very unique situation where we're in Spring Training," Moore said. "These games don't go on our record. ... If I'm not going to get out of the first inning, I want it to be here."
Martin hit his third home run of the spring in the fourth when he crushed a three-run shot to center off Rays closer Grant Balfour. Martin's blast put the Pirates up, 9-1.
Martin has six hits in his last 10 at-bats. Last spring, the catcher had six hits in his first 40 at-bats during Spring Training. He had four RBIs Saturday after collecting just three last spring.
Francisco Liriano started for the Pirates and surrendered a run in the first, when Logan Forsythe tripled to lead off the inning and scored on James Loney's sacrifice fly.
Liriano, who will be the Pirates' Opening Day starter, allowed one run on four hits, walking one and striking out three in three innings.
Jerry Sands hit a two-run homer in the eighth inning for the Rays, and he drove in a run in a two-run ninth.
Up next: Edinson Volquez, who has made two relief appearances, gets his first start against the Orioles in Sarasota, Fla., on Sunday in the road portion of the Bucs' only split-squad games of the spring. Charlie Morton is due to start against the Red Sox in McKechnie Field. Both games have a 1:05 p.m. ET. start, with the home action on MLB.TV and on ROOT Sports for the first of its five preseason telecasts. Travis Ishikawa, who has nursed a strained right hamstring all spring, is scheduled to make his first start as the designated hitter against Boston.