Earlier in the day, the Croats took the lead in front of their home crowd in Zagreb, when Marin Cilic defeated Federico Delbonis.
However, it was far from straightforward for Cilic who, after racing ahead after winning the opening two sets, was pegged back by the spirited Delbonis.
The 2014 US Open champion rallied well though and stormed through the decider to put his country 1-0 up courtesy of a 6-3 7-5 3-6 1-6 6-2 win.
That left the powerful duo of Del Potro and Karlovic to do battle in the second singles rubber of the day and it was another intense affair.
Delpo got the job done, claiming a 6-4 6-7 6-3 7-5 win over his big-serving rival to level the best-of-five tie at one each.
Saturday sees the potentially decisive doubles, with Croatia's Ivan Dodig and Frank Skugor taking on Argentina's Leonardo Mayer and Guido Pella at the Arena Zagreb.