In the afternoon opener, rookie Shane Spencer belted two home runs and Tino Martinez end his batting drought with a home run and four runs batted in as the Yankees outslugged Cleveland 10-4.
Spencer smacked solo homers off the Indians pitcher Dave Burba in the second and fourth innings. The Yankees manager, Joe Torre, said: "I just wanted to get him some at-bats and he's opened some eyes with the power he's shown."
Scott Brosius also slammed a pitch out of the park for the Yankees, who have now slugged 201 home runs this season, the second-highest total in the club's history. The Yankees blasted 240 home runs in 1961 when Roger Maris and Mickey Mantle combined for 115.
In the second game, Ricky Ledee drove in three runs as the Yankees won 5-1.
New York now need to win three of their remaining five games to eclipse the 1954 Indians' American League record of 111 victories.
The Yankees' Chili Davies said: "It's something that's reachable and with only five games left. Why not go for it? That will leave us on a very sweet note going into the playoffs."
At Anaheim, Rick Helling became the third 20-game winner in the major leagues as the Texas Rangers opened a two-game lead in the American League West with a 9-1 rout of the Angels.
The Rangers went into the three-game showdown tied for first place with Anaheim and have come up with back-to-back 9-1 victories.
Helling (20 wins 7 losses) joined Tom Glavine of Atlanta and Roger Clemens of Toronto as baseball's 20-game winners.
In Seattle, Ken Griffey Jnr hit his league-leading 54th and 55th home runs of the season and put himself in some very lofty company by reaching 140 RBI for the third consecutive season as the Mariners edged the Oakland Athletics 7-6.
Griffey smacked a solo blast in the third inning off Jay Witasick and sparked a three-run fifth inning with another solo shot. Griffey, who also scored the winning run in the sixth, joined Yankee legends Babe Ruth and Lou Gehrig as the only players ever to compile 140 RBI in three seasons running.