At New York, Rice smashed a grand slam and a solo homer while right-hander Schlittler mystified the Red Sox, striking out 10 while allowing only two hits over 6 1/3 scoreless innings in a masterpiece 9-0 shutout.
"Just thrilled it left the yard to get four runs," Rice said of his grand slam. "This is what you dream about, Yankees-Red Sox playoff game in New York."
New York seized a 1-0 lead in their AL series, with the winner facing Tampa Bay in round two.
The Yankees, missing slugger Aaron Judge due to a calf strain, saw Rice homer in the fifth, single home a run in the seventh and smash a bases-loaded homer in the eighth.
Austin Wells drove in two runs, Luis Garcia plated a run hitting into a double play and Schlittler threw a career-high 117 pitches to silence Red Sox hitters.