Zagreb - 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.
"The atmosphere was absolutely fantastic as our fans carried us throughout the contest," said Cilic.
Dodig added: "This is a once in a lifetime experience and I have to thank the fans for creating a fantastic atmosphere.
"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.
"Del Potro is an incredibly good player but I am confident I have enough left in the tank to finish the job," added Cilic.
However, should Del Potro extend the tie 37-year-old Karlovic - the oldest player to feature in a Davis Cup singles match since 43-year-old Australian Norman Brookes in 1920 - 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.
Results in the Davis Cup final between Croatia and Argentina in Zagreb on Saturday:
Croatia 2 Argentina 1
Marin Cilic/Ivan Dodig (CRO) bt Juan Martin del Potro/Leonardo Mayer (ARG) 7-6 (7/2), 7-6 (7/4), 6-3
Marin Cilic (CRO) bt Federico Delbonis (ARG) 6-3, 7-5, 3-6, 1-6, 6-2
Juan Martin del Potro (ARG) bt Ivo Karlovic (CRO) 6-4, 6-7 (6/8), 6-3, 7-5
Playing on Sunday:
Marin Cilic (CRO) v Juan Martin del Potro (ARG)
Ivo Karlovic (CRO) v Federico Delbonis (ARG)