The result took away some of the luster of another move up the all-time hit list by New York's Derek Jeter.
Chicago whipped up on five New York pitchers, turning an 8-6 lead into a runaway with six runs over the final three innings.
Ramirez hit a two-run homer in the seventh and had an RBI double during Chicago's four-run ninth. A.J. Pierzynski hit two solo homers and added a third RBI on an infield single in the third.
Chicago won its fourth straight and defeated the Yankees for the second night in a row, having overcome a two-run deficit in the ninth for a victory Thursday.
Jose Quintana (3-1) got the win despite giving up six runs on eight hits in six innings.
New York starter Adam Warren (0-1) also allowed six runs on eight hits, but did so in just 2 1/3 innings.
It was the major league debut for Warren, who was called up after the New York rotation was rocked by injuries.
Jeter led off the New York first with a double for the 3,185th hit of his career. That moved him past Cal Ripken Jr., into 13th place on the all-time hit list. Napoleon Lajoie is 12th on with 3,252 hits.