Nuno (1-0), making his first major league start and second overall appearance, tamed the Indians on three hits while walking three and striking out three.
The 25-year-old left-hander was making a spot start after the Yankees fell to the Indians in the opener 1-0.
Andrew Warren finished up the whitewash with four innings of scoreless relief.
Tribe starter Trevor Bauer (1-2) was touched for three runs (two earned) on six hits over 6 1/3 innings.
Dennis Rodman pledges to end trips to North Korea
Interpol investigating stolen passports on missing flight