The veteran made his first Davis Cup start since 2005 as he earned his 16th victory from 23 rubbers.
Earlier, German Philipp Kohlschreiber clawed the visitors back, beating Fernando Verdasco 6-4, 6-2, 1-6, 2-6, 8-6.
Blake's battering on indoor clay was the second defeat of the weekend for the 29-year-old who lost in the first round at both the French Open and Wimbledon.
His record dropped to 7-10 in live rubbers.
Croatia are the only team with a positive record against the Americans, having won all three of their ties in 2003, 2005 and now at this Adriatic port resort.
The US was trying to recover from 2-0 down for the first time since 1934 but failed spectacularly in the attempt as Blake fell.
Cilic, ranked 15th, called his effort 'one of the best matches I've played'.