Swisher, Curtis Granderson, Russell Martin and Jeter hit solo homers off Franklin Morales (3-4), and Swisher added another solo shot in the seventh against Clayton Mortensen. Jeter's homer gave the Yankees 10 players with 10 or more this season, tying the club record set in 1998.
Phil Hughes (12-10) survived his own throwing error that led to four unearned runs during a rainy third inning. Down 3-0, the Red Sox went ahead on Dustin Pedroia's three-run homer, the 28th long ball off Hughes this year.
New York, which has led the AL East since mid-June, improved to 7-3 against the Red Sox this season. Boston has not won consecutive games since Aug. 5-6.
Hughes allowed four hits in seven innings. David Robertson pitched the eighth and Rafael Soriano finished for his 30th save, completing a five-hitter.
BLUE JAYS 3, RANGERS 2
TORONTO (AP) — Edwin Encarnacion hit his 31st home run, J.A. Happ won his second straight start and Toronto handed Texas its fourth loss in five games.
Happ (2-1) matched a Blue Jays record by striking out six straight batters in the second and third innings. He finished with eight strikeouts in all, allowing one run and two hits in six innings.
Yu Darvish (12-9) struck out 10 in seven innings, but lost for the second time in three starts. He gave up three runs and three hits in seven innings.
He reached double figures in strikeouts for the seventh time this season, tying Jim Bibby (1973) for the Rangers rookie mark.
Casey Janssen got three outs for his 16th save.
TIGERS 5, ORIOLES 3
DETROIT (AP) — Prince Fielder hit a pair of two-run homers to lift Detroit to the victory.
Fielder tied it at 3 with a 462-foot shot to right-centre in the sixth. He then hit a soaring shot to right in the eighth to put the Tigers in front.
Joaquin Benoit (2-3) pitched a perfect eighth inning for the win. Jose Valverde gave up a leadoff double to Manny Machado in the ninth, then retired the next three Orioles for his 23rd save in 27 chances.
Darren O'Day (6-1) took the loss after J.C. Romero allowed Fielder — the first batter he faced — to hit his second homer of the game and No. 22 on the year.
Miguel Cabrera, who scored on both of Fielder's homers, put the Tigers ahead 1-0 in the first inning with his 31st home run.
RAYS 12, ANGELS 3
ANAHEIM, Calif. (AP) — B.J. Upton went 4 for 5 with a home run and three RBIs, Ben Zobrist and Jose Molina also homered and the Tampa Bay Rays battered Jered Weaver for a career-worst nine earned runs.
James Shields (11-7) allowed three runs, seven hits and no walks in six innings while striking out eight, helping the Rays maintain a one-game lead over Detroit and Baltimore in the AL wild-card race. The Orioles lost to the Tigers after starting the day tied with Tampa Bay.
Weaver (15-3) had his shortest outing of the season, giving up eight hits and two walks in three-plus innings — including Zobrist's 14th homer and Upton's 15th.
ROYALS 4, WHITE SOX 2
KANSAS CITY, Mo. (AP) — Salvador Perez hit a tiebreaking two-run double with two out in the seventh inning and Kansas City won for the third time in four games.
Luis Mendoza pitched seven effective innings, and Billy Butler hit his 25th homer for the Royals.
Paul Konerko hit a solo drive for Chicago after being activated from the seven-day concussion disabled list. It was Konerko's first game since he was struck by a Jarrod Dyson elbow while covering first base on Aug. 7 against the Royals.
White Sox ace Chris Sale (14-4) allowed four runs and nine hits in 6 2-3 innings.
Mendoza (7-8) gave up two runs and four hits. Kelvin Herrera worked out of a jam in the eighth and Greg Holland finished for his fifth save in six opportunities.
ATHLETICS 6, INDIANS 4
OAKLAND, Calif. (AP) — Josh Donaldson hit a tiebreaking single with the bases loaded in the eighth inning and Oakland rallied from four runs down.
Chris Carter drew a leadoff walk against Cleveland reliever Joe Smith (7-3) and Brandon Moss followed with a single. Pinch-hitter Josh Reddick then blooped a single into right field off Vinnie Pestano before Donaldson's fourth hit of the night scored pinch-runner Adam Rosales.
Cliff Pennington added a sacrifice fly to cap the outburst for the A's, who pulled within five games of first-place Texas in the AL West and a half-game of the second wild-card spot.
Shelley Duncan hit his first career grand slam for the Indians.
Jordan Norberto (4-1) pitched 1 2-3 innings for the win and Grant Balfour worked the ninth for his 10th save, capping a stellar night for Oakland's bullpen after starter Tommy Milone struggled.
MARINERS 5, TWINS 3
SEATTLE (AP) — John Jaso and Miguel Olivo homered, and Hisashi Iwakuma pitched seven strong innings.
Iwakuma (4-3) gave up four hits, but didn't allow an earned run in winning for the third time in four decisions. He struck out six and walked one for the Mariners, who have won three of four.
Minnesota starter Nick Blackburn struggled again, allowing five runs and 11 hits. Blackburn (4-9) has lost five consecutive decisions and hasn't won since June 22.
Justin Morneau's double to open the fifth inning snapped Seattle's streak of 42 consecutive batters retired, the longest streak in the majors since 1974. The last batter to reach base against the Mariners was Tampa Bay's Jeff Keppinger, who doubled to lead off the ninth inning on Tuesday.