Cilic defeated Blake 6-3, 6-3, 4-6, 6-2 Sunday to help Croatia reach its first Davis Cup semifinals since winning the competition in 2005.
Croatia will take on the Czech Republic at home in September. The Czechs beat Argentina 3-2 on Sunday.
Croatia took a 2-0 lead after Ivo Karlovic rallied to beat Blake and Cilic outlasted Mardy Fish in five sets in Friday's opening singles. Bob and Mike Bryan beat Croatian duo Roko Karanusic and Lovro Zovko in Saturday's doubles.
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