World number 12 Borna Coric put Croatia 1-0 up in the Davis Cup final against hosts France after outplaying world number 40 Jeremy Chardy.
Coric broke serve in the first game and stayed in control to win 6-2 7-5 6-4.
France captain Yannick Noah sprang a surprise by opting for Chardy for the opening singles rather than Lucas Pouille, the highest-ranked player in his squad.
But the gamble backfired for the hosts who are bidding for an 11th win.
France will now hope Jo-Wilfried Tsonga can level the tie when he takes on world number seven Marin Cilic in Friday's second singles match.