Mektic and Pavic win all-Croatian final to take doubles gold
Gold medallists Croatia's Mate Pavic (L) and Croatia's Nikola Mektic celebrate on the podium during the Tokyo 2020 Olympic.
Both duos improved on their country's previous best tennis result at the Olympics, after three bronze medals.
"It's more than a dream come true," said Mektic. "We are delighted."
Cilic, the 2014 US Open champion, and Dodig fought back after losing the first set, but slipped 7-1 down in the breaker.
"This one (title) is definitely a special one. It's tough to beat Wimbledon which was only a couple of weeks ago," added Mektic.
"But this is different, you're not just playing for yourself, you're playing for your country."
Earlier on Friday, Marcus Daniell and Michael Venus became the first New Zealanders to win an Olympic tennis medal for 109 years, beating Americans Austin Krajicek and Tennys Sandgren in the bronze-medal match.
Daniell and Venus won 7-6 (7/3), 6-2 to continue an excellent Tokyo Games for New Zealand.
The only previous tennis medal winner from the country was Anthony Wilding, representing Australasia, who took indoor singles bronze in Stockholm in 1912. The four-time Wimbledon champion was killed during World War I three years later.
"To follow in his footsteps, he was New Zealand's best ever tennis player, is surreal," said Daniell.
"It hasn't sunk in yet, I'm a bit in disbelief. This is going to take some weeks to process."
Daniell and Venus had lost in the semi-finals on Thursday to Cilic and Dodig.
It was New Zealand's eighth medal of the 2020 Olympics so far.
Sandgren and Krajicek's defeat ensured it will be the first time the United States have failed to win an Olympic tennis medal since the 1920 Antwerp Games. Tennis was not on the Olympic programme between 1924 and 1988.
Team USA were without their top four ranked men's players and Serena Williams, Sofia Kenin and Coco Gauff in Japan.