Four-time runners-up Argentina are chasing a first Davis Cup title.
Maradona, 56, who inspired Argentina to glory at the 1986 World Cup, watched on with his girlfriend as Croatia went 1-0 up when Marin Cilic battled back from a mid-match collapse to beat Federico Delbonis 6-3, 7-5, 3-6, 1-6, 6-2 at the Zagreb Arena.
But in the second rubber Del Potro left the final all square when he despatched big-serving 37-year-old giant Karlovic 6-4, 6-7 (6/8), 6-3, 7-5.
It was a fine performance from the Olympic silver medallist, who had secured Argentina's appearance in their fifth final when seeing off Andy Murray -- his Rio conqueror -- in an epic five-setter against the defending champions Great Britain in the semi-final in Glasgow.
Del Potro, 28, is a veteran of two losing finals -- both against Spain in 2008 and 2011 -- while Karlovic is the oldest player to feature in a Davis Cup singles match since 43-year-old Australian Norman Brookes in 1920.
Del Potro was rock solid, allowing the Croat not one break point in the entire match which kept the 15,000-capacity crowd enthalled for three hours and 19 minutes.
He clinched the rubber on his second match point.
"I was nervous after I lost the second set but in the end I had to take the longer road to victory," said Del Potro.
Earlier, former US Open champion Cilic appeared to be cruising towards a routine victory only to lose his way after storming into a two-set lead over the world number 41.
Sixth-ranked Cilic, who made his second appearance at the ATP Tour Finals last week, secured the first two sets with a single break in each, but Delbonis claimed the third before racing through the fourth to force a decider.
Backed by an impassioned crowd, Cilic regained his nerve in the final set, breaking his opponent in the first game and building on that momentum to eventually close out victory in three hours and 30 minutes.
"The crowd helped me to stay in there, it was not easy," said Cilic.
"Federico played a great tennis from the middle of the third set to the end of the fourth. Just at the beginning of the fifth, I tried mentally to stay in there and get that break, and it was a huge difference."
Four-time runners-up Argentina are chasing a first title, while Croatia are looking to emulate their 2005 triumph over Slovakia.
Saturday's doubles are slated to pit Croatian duo Ivan Dodig and Franko Skugor against Leonardo Mayer and Guido Pella, although the line-ups could change.