Moore walked two and gave up a single as the Pirates loaded the bases in the first. He managed to escape the jam, but he threw 25 pitches, of which just 13 went for strikes.
"To find that overall feel for the heater from the get-go was a little tough tonight," said Moore, regarding his command.
That doesn't mean he is getting nervous about his control, however. "I'm pretty competitive," he said. "I feel like it's not so much like you can just turn it on. But when the time comes around and I'm battling in those moments where I have runners in scoring position, it's better when it's going like that."
Russell Martin did not let Moore escape the second. After Kyle McPherson and Jose Tabata strung together back-to-back singles with two outs, the Pirates catcher smoked a ground-rule double to left that drove home McPherson for a 1-0 Pirates lead.
Moore issued a leadoff walk to Gaby Sanchez to start the third. Sanchez moved to second on a wild pitch before Josh Harrison brought him home on a single to left.
Moore allowed two runs on six hits and five walks, while striking out three in 4 2/3 innings before getting lifted after 106 pitches.
McPherson, who is competing for a spot at the back end of the Pirates' rotation, surrendered a solo home run to Shelley Duncan in the second. For Duncan, the blast was his fifth of the spring.
Ben Zobrist put the Rays ahead with a two-run homer with two outs in the fifth off of McPherson. But he didn't leave the yard without a little help from Pirates right fielder Tabata, who may have knocked the ball over the fence as he tried to make a leaping grab.
Matt Joyce followed with a single before Evan Longoria hit his first homer of the spring, driving a 2-0 McPherson offering deep onto the berm past the left-field fence for a 5-2 Rays lead.
"It's good to get [the first home run] out of the way," said Longoria. "I had a couple of good at-bats today where I hit the ball on the barrel, and really that's just been my focus, is having good at-bats. The balls that are in the zone, barreling them up."
McPherson allowed five runs on seven hits -- including the three homers -- and one walk. He struck out two in his five innings of work.
In the sixth, Desmond Jennings drove in James Loney with a single up the middle.
Up Next for the Rays: Roberto Hernandez will start on Tuesday when the Rays travel to Clearwater to play the Phillies in a 1:05 contest. The veteran right-hander is locked in a battle with Jeff Niemann for the No. 5 spot in the starting rotation. Cesar Ramos is also scheduled to see action.