After Kane Williamson's superb innings of 148 set the Windies 292 for victory, New Zealand had their counterpart's in trouble at 164/7 before Brathwaite (102 of 88 balls) steered his side's lower order to six runs of their target.
However, Brathwaite was agonisingly caught at long on by Trent Boult off the bowling of Jimmy Neesham (1-35) to end their hopes of qualifying for the semi-finals.
Meanwhile New Zealand return to the top of the table and can start preparing for the semi-finals, even though they haven't officially qualified yet.
Williamson all class with another century
The Black Caps were put into bat by the Windies captain Jason Holder and immediately ran into trouble, with both Martin Guptill and Colin Munro falling victim to Sheldon Cottrell in the first over.
However, the formidable duo of Williamson and Ross Taylor steered New Zealand away from the dramatic start in a stand worth 160 before Taylor (69) was dismissed by the part-time spin of Chris Gayle.
But Williamson continued to show why he is regarded as one of the best batsmen in the world at this years tournament when registering his second successive hundred and his 13th ODI century.
Cottrell (4-56) impressed with the ball and removed Tom Latham (12) and Colin De Grandhomme (16) but couldn't stop the Kiwis from scoring 92 from the final 10 overs to set a difficult target.
Brathwaite bashes hundred as Windies fall agonisingly short
West Indies' start to their innings fared little better than New Zealand with Boult claiming the scalps of Shai Hope (1) and Nicholas Pooran (1) to leave the Carribbean side facing a daunting task.
But the veteran Gayle (87) and the promising talent Shimron Hetmeyer (54) rebuilt the Windies innings before Hetmeyer fell victim to Lockie Ferguson (3-59) courtesy of a wonderfully deceptive slower ball.
Hetmeyer's dismissal sparked a collapse, with the West Indies losing five wickets for just 22 runs to leave them on the verge of another World Cup defeat.
Brathwaite and Kemar Roach offered some stubborn resistance with a partnership of 47 for the eighth wicket before Roach fell to Matt Henry (1-76), but Brathwaite, Cottrell and Oshane Thomas kept plugging away to set up a golden chance for an unlikely victory.
Brathwaite looked set to defy the odds when smashing 24 off Henry's final over and bring up his century, in turn leaving the Windies requiring just six to win.
However, Brathwaite couldn't match his 2016 Twenty20 World Cup Final heroics and his ecstasy turned to agony when shelling out to Trent Boult in a bid to finish an action-packed match with a six.
While Brathwaite fell to his knees in heartbreak, New Zealand celebrated a pulsating victory knowing that they have realistically booked their semi-final berth in consecutive World Cups.