Set a challenging target of 271 after wicketkeeper Matthew Wade's unbeaten 57 led an Australian lower-order revival from 173 for six to a final total of 270 for nine off 50 overs, Marsh claimed the prized wickets of Darren Bravo and Marlon Samuels, adding the scalp of opening batsman Johnson Charles for good measure to effectively short-circuit the home side's pursuit.
His disciplined medium-pacers realised miserly figures of three for 32 with the West Indies unable to recapture the impressive batting form of earlier matches in being dismissed for 212 off 45.4 overs at Kensington Oval in Barbados on Sunday.
Josh Hazlewood polished off the tail to finish with the best figures of five for 50, but it was Marsh's spell that made the difference when it mattered most.
"We really fought well tonight and I always felt we could defend that total," said victorious captain Steve Smith. "It's just the way we play. We believe in ourselves and go hard at the opposition every time."
Charles topscored with 45 and featured in an encouraging opening partnership of 49 with Andre Fletcher.
They weathered the early assault from Mitchell Starc but it was fellow new ball bowler Hazlewood who prised out Fletcher in the 11th over of the innings.
Marsh, adjudged Man of the Match, then cemented Australia's control of the match when he had Bravo caught behind, Samuels taken at short extra-cover and Charles leg-before within the space of ten runs.
At 72 for four and with the top batsmen gone, West Indies' chances of victory had lurched into improbability, especially when leg-spinner Adam Zampa lured the big-hitting Kieron Pollard into hoisting a catch to long-off.
Like his Australian counterpart, Denesh Ramdin attempted to engineer a recovery. His captain, Jason Holder, dominated a 43-run stand in contributing 34 before falling to Nathan Coulter-Nile.
A couple big hits by Carlos Brathwaite then generated some excitement before he was bowled by Hazlewood and from that point on, the favourites closed out the match, Ramdin being eighth out for 40.
Hazelwood took the Man of the Series honours.
Ironically, it was Marsh's dismissal to spinner Sulieman Benn in the 37th over that raised Caribbean hopes of upsetting the five-time World Cup-winners who were then in danger of being dismissed for under 200 and confounding Steve Smith's decision to bat first.
Yet Wade somehow managed to survive against his nemesis, mystery spinner Sunil Narine, and prospered against the seamers, crashing three sixes to complete a recovery that saw 97 runs added over the last 13 overs.
West Indies were hampered by the absence of Shannon Gabriel at the end of the innings with the tearaway fast bowler leaving the field after completing seven overs.
"We missed having Shannon available at the end of the innings," Holder observed. "I felt he was our best chance of knocking off their lower order."
His first four overs had proved expensive but Gabriel returned midway through the innings to account for Smith (46) and the dangerous Glenn Maxwell in the same over.
Aaron Finch led the charge at Gabriel with a robust knock of 47, his highest ODI score against the West Indies. He looked set for a big innings when a miscued heave off Pollard offered Samuels a simple catch on the square-leg boundary.
Holder returned in the midst of the lower-order rally to snare Coulter-Nile, however the captain appeared to have miscalculated his bowling options in only allowing Brathwaite eight of a possible ten overs.