Jake Fraser-McGurk slammed 41 off 18 balls as Australia chased down 87-run target in 6.5 overs — a record for their shortest successful chase in the format.
The hosts had already won the series after bagging victory in the first match in Melbourne by eight wickets and the second in Sydney by 83 runs to claim the series.
West Indies crumbled to 86 all out, a record low ODI total at Manuka Oval, in the 25th over after Australia skipper Steve Smith won the toss and opted to bowl first despite an attack missing Josh Hazlewood, Pat Cummins and Mitchell Starc.
In reply, Australia raced to the target with 259 balls remaining to complete a stunning capitulation by the Caribbean side.
The 21-year-old Fraser-McGurk showed impressed one and all in only his second match with five fours and three sixes in a brisk 41 before he was caught going for another big hit off Alzarri Joseph.
Aaron Hardie was the only other wicket to fall, caught behind for two off Oshane Thomas.
Josh Inglis blasted an unbeaten 35 while Smith was not out six.
Earlier, paceman Xavier Bartlett took 4-21 to go with the 4-17 he bagged on his debut in Melbourne. Fellow fast bowler Lance Morris grabbed 2-13 before leaving the field with a side strain.
Bartlett struck early with Kjorn Ottley trapped lbw for eight and, while Athanaze and Keacy Carty steadied the ship, they were in survival mode, with just 36 runs coming from the opening 10 overs.
Their partnership ended when Morris was introduced and grabbed his first international wicket, courtesy of Marnus Labuschagne holding a spectacular diving catch at point to remove Carty for 10.
Skipper Shai Hope needed a big score and drove Morris to the ropes, but he lasted just five balls before falling lbw to Shaun Abbott, leaving the visitors in trouble on 43-3.
Debutant Teddy Bishop soon followed for a duck, undone by the sheer pace of Morris whose fullish ball clattered the middle stump before he left the field midway through his fifth over.
Athanaze was the one shining light, making a battling 32 off 60 balls before mis-hitting a sweep off spinner Adam Zampa with Abbott collecting a simple catch.
Two more wickets in three balls left the West Indies reeling, with Romario Shepherd out for a golden duck to Bartlett and Matthew Forde run out after a comical mix-up with Roston Chase.
Bartlett then cleaned up the tail with two more wickets.