Russell came up in the next half-inning and smacked a 3-2 pitch from Jon Rauch (3-6) into the seats in the left field corner of Yankee Stadium for his second homer of the day.
His first clout, a two-run shot, came in the seventh and helped the Yankees cut into a 3-0 Mets lead. The Yanks went ahead in the eighth on four straight singles, including run-scoring hits from Marx Teixeira and Alex Rodriguez.
Boone Logan (1-0) earned the victory after quelling the Mets' ninth-inning rally.
Mets starter Jonathon Niese yielded only two unearned runs on seven hits over seven innings.
The Mets lost for the sixth time in seven games.