It is the longest win streak in Major League Baseball this season and leaves the Red Sox one victory shy of matching their club record of 15 set in 1946.
Third baseman Durbin blasted a pitch from Orioles reliever Tyler Wells into the seats atop Fenway Park's "Green Monster" left-field wall with two outs in the eighth inning. It was his 10th homer of the season.
Boston closing relief pitcher Aroldis Chapman, a 38-year-old Cuban left-hander, walked Colton Cowser and surrendered a two-out double to Gunnar Henderson that put two Orioles runners in scoring position in the ninth.
Baltimore's Tyler O'Neill then smacked a line drive that was caught by Taiwanese shortstop Cheng Tsung-che of the Red Sox for the final out to secure the triumph.
The visiting Orioles were undone by four errors, their most in a game since 2023.
The Red Sox, founded in 1901, can set a club record by sweeping the three-game series with Baltimore, which saw a seven-game win streak snapped.
Boston improved to 51-48, clinging to the final American League wildcard playoff spot with two months remaining in the campaign with Baltimore three games back at 49-52.