It was an unusual start to the work day for Tillman. Showalter said the right-hander and fellow pitcher Miguel Gonzalez were in a very minor accident when the taxi they were riding in was tapped from behind en route to the ballpark.
Davis homered on a 3-0 pitch into the bleachers behind Boston's bullpen to push Baltimore ahead 1-0 in the second.
Boston jumped in front 2-1 in the third on the run-scoring singles by Pedroia and Napoli.
But the Orioles tied it against Aceves in the fifth when Jones had a two-out RBI single after Machado reached on a bunt single and advanced to second when he was running on the pitch on Markakis' bouncer to third.
Red Sox right-hander Alex Wilson made his major league debut, working a scoreless ninth with a walk.
NOTES: Farrell said he talked a bit with closer Joel Hanrahan "about going forward." The right-hander gave up five runs and only got two outs in the ninth inning of Wednesday's 8-5 loss. "He's our closer," Farrell said. ... Showalter is one who thinks Fenway's dugouts are a bit small. He said before the game that he let the four other starting pitchers go into the clubhouse to watch the later part of Wednesday's game to open some room for others to sit. ... Red Sox DH David Ortiz, who missed all of spring training with a sore right Achilles, went 2 for 3 with two singles, an RBI and scored a run in first rehab start for Triple-A Pawtucket on Thursday. "We feel 20 or so (at-bats) are needed and then we'll reassess," Farrell said. ... There was an unusual 3-5-3 play when the left-handed batting Davis hit into a shift and the ball caromed off 1B Napoli over to 3B Will Middlebrooks, who was shifted to the right side. He then threw back to Napoli. ... Boston's Felix Doubront (0-0) is slated to face Alex Cobb (1-0) in the opener of a four-game series against Tampa Bay on Friday at Fenway.