Croatia sealed their ticket to the Davis Cup final after Marin Cilic's three sets victory over Richard Gasquet gave them an unassailable 3-1 lead over nine-time champions France in Zadar.
Croatia, titleholders only once in 2005, will face the winner of the other semi-final between holders Great Britain and Argentina in the November final.
Cilic bagged the all important point in the first of Sunday's reverse singles, seeing off Gasquet 6-3, 6-2, 7-5.
"When you look at the atmosphere, it's an incredible feeling. It's been a dream weekend for us," said 2014 US Open winner Cilic.
"I played incredible tennis. I produced a great performance for all the crowd."
Gasquet, 17th in the world, was drafted in after Jo-Wilfried Tsonga and Gael Monfils pulled out with knee injuries.
The 30-year-old Gasquet, initially overlooked by captain Yannick Noah after struggling with back and chest injuries, claimed the opening singles 6-2, 7-6 (7/5), 6-1 against Borna Coric.
But world number 11 Cilic hit back against Lucas Pouille 6-1, 7-6 (7/4), 2-6, 6-2 to put the Croats level.
Croatia had taken command of the tie in Saturday's doubles when Cilic and Ivan Dodig downed top-ranked French pair Pierre-Hugues Herbert and Nicolas Mahut 7-6 (8/6), 5-7, 7-6 (8/6), 6-3.
Croatia's previous Davis Cup success came 11 years ago at the expense of Slovakia.