Corey Kluber tossed a dominant six innings, striking out nine and Roberto Perez drove in four as Cleveland took game one convincingly.
The Cubs looked overmatched all game long, striking out 13 times and collecting only nine base-runners.
Jon Lester lasted 5.2 innings, but allowed three runs off of six hits and three walks. The score remained 3-0 until Perez hit his second homer of the evening, to make it 6-0.
The Cubs were similarly shut out 6-0 in game three against the Los Angeles Dodgers in the NLCS but came back to win the next three games, scoring 23 runs in those games.
The series resumes Wednesday as Jake Arrieta faces off against Trevor Bauer.