Neither starter was especially sharp, with Aceves and Alex Cobb each allowing two runs in two innings. It was the Grapefruit League debut for both.
Dustin Pedroia staked Aceves to a 1-0 lead with a homer in the top of the first, but it didn't last. Aceves had difficulty finding the strike zone early, and it cost him. He walked the second and third Rays batters of the game. The fourth was Yunel Escobar, who got ahead of Aceves, 2-0, before drilling a two-run double to left field.
Aceves settled down after that, retiring five of the last six batters he faced. He finished with two runs on two hits, no strikeouts and the two walks. He did induce four ground-ball outs.
Cobb, meanwhile, was scored upon in each of his two innings. Pedroia cranked a solo homer deep to left in the first, and Mike Carp made his Red Sox debut a good one with an RBI double in the second.
"Obviously the results weren't great, but this time of year I'm looking to feel good, and I did," Cobb said. "The home run isn't very good, and the RBI double wasn't very good, but I got a lot of ground balls, which is what I'm looking for."
After Cobb came out, the Rays' bullpen took command. Jamey Wright struck out two in a perfect third inning, and Cesar Ramos retired all six batters he faced. No Tampa Bay reliever allowed a hit until Boston managed a run on two hits against Neil Schenk in the eighth.
Tampa Bay improved to 3-1 on the spring. Boston is 2-2.
Up next for the Rays: Reigning American League Cy Young Award winner David Price will make his first outing of the spring in Tuesday's 1:05 p.m. ET game against the Astros. He is expected to pitch one inning. Also seeing action will be right-handers Kyle Farnsworth, Fernando Rodney, Brandon Gomes and Alex Colome, along with left-handers Mike Montgomery and Enny Romero. Right-hander Jordan Lyles will start for Houston.
Matthew Leach is a writer for MLB.com. Read his blog, Obviously, You're Not a Golfer and follow him on Twitter at @MatthewHLeach. This story was not subject to the approval of Major League Baseball or its clubs.