Croatia's Marin Cilic upset France to earn a straight sets win (7-6, 6-3, 6-3) against against Pouille to win his country's second Davis Cup after setting up the win on Saturday with a similarly dominant performance.
Cilic, the world's seventh-ranked player, eased to victory in the final two sets after a close affair in the first in which the world number 32 Pouille brought his opponent to the wire, eventually coming up short by 7 games to 6.
The overall score in the final was 3-1 to the Croatians.
The final two sets were much more straightforward affairs, with Cilic pulling away as his opponent failed to sustain a comeback.
This is a blow to French tennis as a whole, as the defending champions failed to repeat their heroics from the previous tournament on home soil.
The Croatian victory will see them as the final champions of the tournament in its current guise, as widespread rule changes are set to take over next year.
Cilic also won his match on Friday as his team set up Sunday's victory - and their first Davis Cup since 2005.
A doubles victory by France earlier on Sunday had kept French hopes alive but, ultimately, Lucas Pouille was unable to bridge the gap.
Pouille, who has had a disappointing 2018, was drafted in to face Cilic by French team captain Yannick Noah as a replacement for Jeremy Chardy who was easily beaten by Borna Coric on Friday.
The Frenchman harnessed the support of the partisan crowd early, scoring six aces in the first set alone as Cilic endured a sluggish start.
However, the Croatian would soon find his feet and rallied to a tie-break in the first stanza. His four unanswered points which would claim him the first set would set the tone for the rest of the match.
The victory will be a sweet one for Croatia's star man. In 2016 he was one set away from another Davis Cup victory before being undone by Argentina's Juan Martin del Potro.
There was no such calamity this time, however, and Cilic never looked in danger of letting his opponent back into the match once he found his rhythm.
Croatian president Kolinda Grabar-Kitarovic, who caused a flurry of headlines as she supported the Croatian side on their journey to last summer's World Cup Final in Russia, was again watching on for her country's latest sporting triumph. It was reported that she spent her own funds on traveling to and attending the match.