Cesar Ramos went 5 1/3 innings for the save.
Ben Zobrist's infield grounder in the first drove in the first run -- and was the Rays' only RBI as they built a 4-1 lead. Three other runs scored on a wild pitch and errors by Pittsburgh outfielders Chris Dickerson and Travis Snider.
Furthermore, two of the Pirates' tallies came in on a wild pitch and an infield grounder, meaning only one of the game's first seven runs scored on a base hit.
One of the hits off Odorizzi was Robert Andino's RBI double in the second. Odorizzi walked three and struck out two in lowering his spring ERA to 2.25 for eight innings.
The Rays were managed by bench coach Dave Martinez as Joe Maddon skippered another squad against the Blue Jays in Port Charlotte, Fla.; they were the Rays' only split-squad games of the spring.
Signed as a free agent for $5 million, Volquez lowered his ERA from 14.29 to 11.00 and ended his outing in encouraging fashion by retiring the last four men he faced.
"The number doesn't look good," Volquez said with a smile, alluding to the overall ERA. "But they love what I've been doing. I've been working on my fastball command and I threw a lot of first-pitch strikes today, so I'm very happy right now."
Up next: David Price will start Sunday afternoon, when the Rays host the Red Sox in a 1:05 p.m. ET contest at Charlotte Sports Park (live on MLB.TV). Price, who will be the Rays' Opening Day starter, will be making his third official start of the spring. Right-hander Allen Webster is scheduled to start for the Red Sox.
Tom Singer is a reporter for MLB.com and writes an MLBlog Change for a Nickel. He can also be found on Twitter @Tom_Singer. This story was not subject to the approval of Major League Baseball or its clubs.