Hanley Ramirez hit a three-run homer and two hits for Boston, which needs to win Monday's annual Patriots' Day game to avoid losing its first series.
Miguel Gonzalez (2-1) pitched five innings for the victory, allowing three runs and five hits.
Rick Porcello (1-2) allowed eight runs and 12 hits -- with two homers -- in five innings.
Jones also equaled his career best with four hits.
Boston DH David Ortiz was ejected by home plate umpire John Tumpane, who replaced original plate ump Paul Emmel.
Jones' three-run double off the left-center field wall chased Porcello and made it 8-3 in the sixth.
Trailing 2-0, Boston jumped ahead on Ramirez's homer that caromed off a billboard above the Green Monster seats and onto the field. Flaherty's home run tied it at 3-3.
Jones' homer went completely out of Fenway Park, clearing the Monster seats, in the first.
Emmel left the game in the middle of the fourth inning, walking slowly to Boston's dugout where he chatted with a member of the medical staff before heading down the steps. There was no announcement why he left.
Second-base ump Tumpane moved behind the plate.
Orioles: Their lineup looks a lot different due to players being on the disabled list. 2B Jonathan Schoop (strained right knee), SS J.J. Hardy (strained left shoulder), C Matt Wieters (right elbow reconstructive surgery) are out.
Red Sox: 2B Dustin Pedroia was rested on Sunday after going 0 for 4 with two strikeouts in Saturday's loss. Brock Holt (11 for 19 coming into the game) started in his place and batted leadoff. He went 1 for 5.
Orioles: Wei-Yen Chen (0-0, 4.35 ERA) is scheduled to start the series finale. In his previous start in Fenway, on Sept. 10, the left-hander had a no-hitter broken up with two outs in the sixth inning.
Red Sox: RHP Justin Masterson (1-0, 7.59) is slated to go for the Red Sox in the annual Patriots' Day game with a scheduled 11:05 a.m. first pitch. He was chased in the fifth inning of his previous start, on Tuesday against Washington, when he gave up seven runs in 4 2/3 innings.