Asked to bat first on a flat pitch at Trent Bridge, champions Australia got off to a terrible start as they were reduced to 79-5 before Coulter-Nile (92) and Smith (73) staged a rescue act with a 102-run stand for the seventh wicket.
Wicketkeeper-batsman Alex Carey (45) had earlier combined with Smith to arrest the slide, after Oshane Thomas, Sheldon Cottrell and Andre Russell put the Windies in a commanding position with their fiery pace in the opening hour.
The trio finished with two wickets each, before Coulter-Nile stole the show with the highest World Cup score for a number eight batsman, eclipsing Zimbabwean Heath Streak's unbeaten 72 in 2003.
The 31-year-old Australian was eight runs short of his maiden century when he was removed by Carlos Brathwaite, who cleaned up the lower order to finish with figures of 3-67.
(Reporting by Hardik Vyas in Bengaluru, editing by Pritha Sarkar)
