Atlanta and the Los Angeles Dodgers, who hold comfortable leads in their NL divisions, both lost.
Boston's Saltalamacchia also doubled and scored twice while David Ortiz and Stephen Drew each doubled twice for the Red Sox, who are careering away to the AL East title after notching their 15th win in 19 games.
Koji Uehara preserved Boston lead with a perfect ninth inning. He has retired 37 straight batters; the longest streak by a reliever in six years.
New York's loss gave some breathing space to Tampa Bay, which was led to a 3-0 win over Minnesota by Chris Archer pitching six scoreless innings.
Archer (9-7) scattered three singles and struck out seven without a walk, following a pair of rough outings for the rookie to start September.
Cleveland moved ahead of the Yankees in the wild-card pecking order by beating the Chicago White Sox 3-1.
Indians starter Danny Salazar struck out nine in 3 2-3 innings, working on a limited pitch count.
Ryan Raburn hit an RBI double for Cleveland, which beat Chicago for the 10th time in a row this season.
Baltimore revived its flagging playoff hopes with a 5-3 win over Toronto, as Chris Davis hit his major league-leading 50th home run of the season, a tiebreaking solo shot in the eighth inning.
Davis became the 27th major leaguer to join the 50-homer club, and the first since Jose Bautista in 2010. Davis led off the eighth with a blast to center.
The drive matched Brady Anderson's 1996 Orioles record tally and made Davis just the third player in major league history with 50 homers and 40 doubles in the same season. The others were Babe Ruth (1921) and Albert Belle (1995).
Detroit's Prince Fielder homered and drove in three runs to power the Tigers to a 6-3 victory over Kansas City.
Detroit remained six games ahead of second-place Cleveland in the AL Central and dealt the third-place Royals a setback in the postseason race. Kansas City is now 3-1/2 games behind Tampa Bay.
Tigers' starter Justin Verlander (13-11) allowed three runs in 6 2-3 innings.
Oakland's Yoenis Cespedes hit a three-run homer in the first inning, and Oakland survived a shaky night from the bullpen to beat Texas 9-8 and stretch its division lead.
Cespedes' homer came off Derek Holland (9-9), who is winless in a career-worst seven straight starts.
The Rangers scored six runs in the eighth inning to close within a run and threaten an important comeback but fell short and suffered their fourth-straight loss.
St. Louis reclaimed the NL Central lead with 2-1 win over Seattle, as Pete Kozma scored on a passed ball with the bases loaded and two outs in the 10th inning.
Kozma entered in the eighth inning as a pinch-runner, later stole third base and scored the tying run.
In the 10th, Kozma singled with two outs off Chase Ruffin (0-2). After two walks loaded the bases, catcher Mike Zunino could not handle Oliver Perez' first pitch to Matt Holliday, with the ball rolling free and Kozma scoring on a head-first slide.
Pittsburgh slipped a game behind the Cardinals after a 5-4 loss to the Chicago Cubs.
Chicago's Anthony Rizzo hit a towering go-ahead, two-run homer off Jason Grilli (0-2) in the seventh inning.
The Pirates lost for just the fourth time in 65 games when leading after six innings this season.
Cincinnati trails St. Louis by 3-1/2 games after a 5-1 defeat by Milwaukee.
Carlos Gomez went 3 for 4 with 5 RBIs for the Brewers.
Milwaukee starter Kyle Lohse (10-9) retired 23 consecutive batters during one stretch. He started the season slowly after missing most of spring training but since then has gone 9-3.
San Diego's Chase Headley hit a tying homer and Logan Forsythe drove in the go-ahead run in a two-run eighth which lifted the Padres to a 4-3 win over Atlanta.
San Francisco's Madison Bumgarner outdueled Clayton Kershaw and held on for a 4-2 win over the Los Angeles Dodgers.
Washington's Wilson Ramos homered and drove in three runs to lead the Nationals to a 6-1 win over Philadelphia and their seventh straight win.
Colorado's Corey Dickerson hit a pitch that bounced well in front of the plate for a double, starting a five-run burst in the seventh inning that led the Rockies over Arizona 7-5.
Houston's Jose Altuve hit a three-run homer and Matt Dominguez's grand slam powered a big fifth inning to give the Astros a 9-7 win over the Los Angeles Angels.
New York's Lucas Duda hit a three-run homer to help the Mets edge Miami 4-3.