Red Sox infielder Pedro Ciriaco looped a single to right field leading off the ninth inning, and errors by right fielder Zoilo Almonte and second baseman David Adams allowed Ciriaco to trot home with what would be the game's only run.
Yankees starter Ivan Nova bounced back from a pair of erratic outings to open his spring, harnessing command of his fastball to hurl four innings of scoreless, two-hit ball, walking none and striking out three. Nova threw 35 of 55 pitches for strikes.
Launching his bid to be the Red Sox's fifth starter, left-hander Felix Doubront turned in an impressive outing, holding New York scoreless on two hits over four innings. Doubront walked one and struck out three with a balk, throwing 49 of 75 pitches for strikes.
"He's been working hard on trying to go after hitters and throwing in the strike zone early and kind of expanding later, so I think tonight was a confidence-booster for him," Red Sox catcher Jarrod Saltalamacchia said of Doubront.
Mariano Rivera made his second spring appearance for the Yankees, pitching a scoreless fifth inning around a Bill Hall throwing error.
Receiving another standing ovation upon entry, Rivera shattered Lars Anderson's bat -- the closer's first broken bat of the spring -- and struck out Alex Hassan looking to finish his 13-pitch, nine-strike effort.
Red Sox right-hander Michael Bowden struck out three of the four batters he faced in a scoreless fifth frame, and righty Vicente Padilla -- competing with Doubront for a rotation spot -- struck out four over three innings.
Yankees left-hander Boone Logan struck out one in a perfect top of the sixth.
Up next: Boston get a day off Wednesday before welcoming the defending World Series champion Cardinals to Fenway South at JetBlue Park in Fort Myers, Fla., on Thursday. Right-hander Alfredo Aceves will get the start against St. Louis and be followed by Daniel Bard, right-hander Matt Albers and lefty Justin Thomas. Righty Kyle Lohse will start for the Cardinals and be followed by closer Jason Motte, Kyle McClellan, Fernando Salas, J.C. Romero and lefty Marc Rzepczynski.