Derek Jeter drove in one of two runs in the sixth, padding the lead to 13-9.
Justin Verlander (10-15) lasted a career-low 1 2-3 innings and gave up eight runs - five earned - and seven hits with two walks.
Brian Bruney (2-0) was credited with the win for pitching 1 2-3 scoreless innings in the middle of the game. Sidney Ponson started and gave up seven runs - six earned - and nine hits over three innings.
In his major league debut, Phil Coke struck out Cabrera with one on to get out of the seventh inning to maintain New York's four-run lead.
The Yankees and Tigers played a makeup game after a matchup in May was rained out. The teams with the highest payrolls in baseball combined for a performance that seemed as significant as a Grapefruit League exhibition. New York's opening-day payroll, counting players on the disabled list, was $209.1 million and Detroit's was $138.7 million.
Both underachieving teams began the final month with double-digit deficits in their divisions.
Perhaps the only intriguing moment happened in the second inning when Ivan Rodriguez came to the plate for the first time against the Tigers since they traded him, and the catcher was greeted with a standing ovation. He acknowledged the fans by taking off his helmet and waving to the sold-out crowd.
Rodriguez signed with the Tigers after they lost an AL-record 119 games in 2004, then helped them reach the World Series in 2006.
Notes: The Yankees expect to activate RHP Joba Chamberlain (rotator cuff tendinitis) from the DL on Tuesday. They plan to use him in the bullpen for the rest of this season, letting him build up arm strength before becoming a starter again in the future. ... The Tigers will pitch LHP Dontrelle Willis and RHP Freddy Garcia against each other in a simulated game before Tuesday's series opener against the Los Angeles Angels. ... Sheffield's 494th homer moved him past Lou Gehrig and Fred McGriff for 25th on baseball's all-time list. ... In a six-day stretch, the Yankees will have played in New York, Detroit, Tampa Bay and Seattle. ... Cabrera has hit 22 of his 30 homers since June 10. ... The Tigers traded Rodriguez to New York for RHP Kyle Farnsworth at the non-waiver trading deadline. ... Retired Michigan football coach Lloyd Carr threw the ceremonial first pitch, then pumped his fist.
