Del Potro, the world's 10th-ranked player, had little trouble dispatching Cilic as the Argentine squad attempts to secure a return trip to the finals, where they lost last year to Spain.
Del Potro's reverse singles win gave his country an insurmountable 3-1 lead in the best-of-five tie.
It also helped clinch home-court advantage over Argentina's opponent in the September semifinals -- the Czech Republic, which bested Serbia Sunday to advance.
Argentina, which remains without a Davis Cup championship after four times as runner-up, improved to 3-0 all-time versus Croatia.
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