Norris blasted a three-run homer and also had an RBI double in support of Bartolo Colon (8-2), who won his fifth consecutive start.
Colon held the Yankees to three hits and four walks while striking out three in six innings. Grant Balfour picked up the save.
CC Sabathia (6-5) was handed the loss after allowing six runs on eight hits over six innings. Mark Teixeira drove in three runs and Vernon Wells accounted for the other run for the Yanks, who had won their previous two games.