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.
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.
"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.
"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.
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