Marin Cilic and Ivan Dodig beat Argentine pair Juan Martin del Potro and Leonardo Mayer 7-6 (7/2), 7-6 (7/4, 6-3 in Saturday's doubles to put Croatia 2-1 up in the Davis Cup final.
Former US Open champion Cilic gave Croatia the upper hand in Zagreb by winning Friday's opening singles rubber against Federico Delbonis before Del Potro levelled for Argentina with a four-set win over Ivo Karlovic.
Both Cilic and Del Potro were drafted in for Saturday's doubles with the former teaming up with Dodig to claim the first two sets in a tie-break before wrapping up victory after Mayer dropped serve at 3-2 down in the third.
"This is a once in a lifetime experience and I have to thank the fans for creating a fantastic atmosphere," said Dodig.
"We will be rooting for Marin to finish the job tomorrow."
Olympic silver medallist Del Potro, who has bounced back after two injury-ravaged seasons, must beat sixth-ranked Cilic in Sunday's reverse singles to keep alive Argentine hopes of a first Davis Cup title.
Karlovic and Delbonis would then face off in the deciding rubber.
Croatia defeated Slovakia in 2005 for the country's only Davis Cup title, while Argentina – beaten by Spain in both 2008 and 2011 – have finished runners-up four times.