Note that the current Davis Cup was last held under the old format, when the competition lasts for six months.
Coric was relentless though and at 5-5 he forged three break points after some terrific scrambling and Chardy, who had saved break points at 3-3, succumbed with a weak backhand.
Cilic dictated matters in the tie-break at the end of a first set, in which Pouille twice held after saving break points, the 2014 US Open champion producing a fine off-balance backhand volley to forge ahead.
"I didn't lose my serve in the match and I played outstanding tennis throughout", said Cilic.
The mainly French 22,000 crowd kept roaring their support for Pouille, but it was the Croatia contingent, decked out in their distinctive red and white, who would soon be celebrating.
"I am able to play all three days".
Croatia claimed a second title in the team event following its first win in 2005.
Croatia's sports-mad President Kolinda Grabar-Kitarovic was among the fans at courtside to savour a landmark title.
"For us, it's a dream come true, for this nation, we are so passionate", he added.
Former players and commentators however, railed against the changes and have expressed their sadness at what they see as the demise of the competition. "In Croatia, it's going to be incredible too".
Croatia had last won the Davis Cup when they beat Slovakia 3-2 in the final in Bratislava.
France's Davis Cup captain Yannick Noah, who oversaw his last Davis Cup match this weekend and will be replaced by Amelie Mauresmo, is also a fervent opponent of the overhaul.
Pouille, surprisingly left out of the opening singles rubbers on Friday despite his world ranking of 32 being the highest of the players available to Noah, will face world number seven Marin Cilic.
After Nicolas Mahut and Pierre-Hugues Herbert won Saturday's doubles, France trailed 2-1 and needed to win both reverse singles on the final day to become the first team since 1939 - when Australia beat the United States - to overturn a 2-0 deficit in a final. I thought Lucas started well in the first set and just a single point made the difference.
He opened a 5-3 lead then latched onto a Pouille serve to crush a forehand victor before converting his first set point with a dropshot of his own.
An animated Noah was up and down out of his seat, firing up his man and the crowd.
The 31-year-old Frenchman fought back gamely in the second set, though, to lead 5-4.
He squandered a two-set lead in the fourth rubber of the final against Argentina's Juan Martin del Potro in 2016 - a defeat that cost Croatia the title.