"First time out, I'm not really disappointed," Tillman said. "I felt OK. Command was spotty, at best. I guess you kind of expect it for first time out. Other than that, I felt pretty good."
Tillman, who is out of options, is projected to be in the rotation. He threw 43 pitches (25 strikes), including a game-opening strikeout of Jacoby Ellsbury.
Boston third baseman Will Middlebrooks exited the game in the first inning after trying to check his swing on an up-and-in fastball from Tillman. He immediately dropped his bat and clutched his right wrist, flinging his helmet into the dugout as he walked off the field. Middlebrooks, who fractured the same wrist last August, was diagnosed with soreness in the wrist and will be re-evaluated on Thursday.
Middlebrooks was replaced by Pedro Ciriaco, whose error in the second inning allowed Adam Jones to reach base and later score on Matt Wieters' single. But Ciriaco rebounded with an RBI single off Orioles bullpen hopeful Daniel Schlereth in the third.
Red Sox reliever Franklin Morales, who made the start, pitched a 1-2-3 first inning. Right-hander Joel Hanrahan surrendered a run in the second inning, and former Oriole Koji Uehara picked up a pair of strikeouts in the third.
Jonny Gomes gave the Red Sox a one-run edge with a leadoff homer off Zach Britton to start the fourth inning. Britton, who is competing for a rotation spot, rebounded nicely and escaped the inning with a double play. He picked up a pair of strikeouts in the fifth -- both looking -- and needed just 11 pitches to get through his second frame.
Baltimore regained the lead in the sixth inning, when Chris Davis connected on a two-run homer off Junichi Tazawa. Taylor Teagarden's two-run single in the seventh gave the O's some insurance.
Up next: Right-hander Jair Jurrjens will make his second spring start, with the plan for him to pitch two innings, against the Twins in Thursday's 1:05 p.m. ET contest. Tommy Hunter and Kevin Gausman are also slated to throw multiple innings. The Twins will start right-hander Liam Hendriks.
Brittany Ghiroli is a reporter for MLB.com. Read her blog, Britt's Bird Watch, and follow her on Twitter @britt_ghiroli. This story was not subject to the approval of Major League Baseball or its clubs.