Australia 270 for 9 (Wade 57*, Holder 2-51, Gabriel 2-58) beat West Indies 212 (Charles 45, Hazlewood 5-50, Marsh 3-32) by 58 runs
Scorecard and ball-by-ball details
Marsh's emergence as a performer under pressure was a major positive of Australia's otherwise workman-like defeat of West Indies and the already vanquished South Africa, making it fitting that he landed the decisive blows against a doughty home side.
A spell of 3 for 6 featured the wickets of Darren Bravo, Marlon Samuels and Johnson Charles in successive overs, breaking the back of the West Indies chase and leaving too much for their heavy-hitting lower order to do. Josh Hazlewood followed up with five wickets of his own, the finishing touch arriving with a typically mercurial catch by Glenn Maxwell.
Australia also owed much to the wicketkeeper Matthew Wade, who muscled his way to a half-century with the tail that atoned for earlier wasted starts by the top order, while also reaffirming his place in the team. Wade's late hitting stretched the total to 270 when at one point 240 looked more likely.
Following a decent start on a slowing pitch in Bridgetown, the visitors' middle order fell away and the tail was left to scratch around against tight bowling by Carlos Brathwaite, Jason Holder and Sulieman Benn. From 152 for 3 in the 31st over, Australia lost 4 for 59 in 13.2 overs before the wicketkeeper Matthew Wade staged a punchy rearguard - his first meaningful innings of the tournament.
Usman Khawaja, Aaron Finch, George Bailey, the captain Steven Smith and Mitchell Marsh were all left to rue their dismissals after making starts. Maxwell was unable to halt the slide, falling to Shannon Gabriel's well-directed pace in the same over as Smith.
Those wickets left Wade in the company of the bowlers, after the selector on duty Trevor Hohns and the interim coach Justin Langer made a significant departure from previous policy by dropping the allrounder James Faulkner.
Man of the match in last year's World Cup final, Faulkner's recent form with the ball has disappointed, and he has had relatively few opportunities to showcase his late innings batting due to the performances of others. Instead, Hohns and Langer plumped for the pace of Nathan Coulter-Nile alongside a recall for the wristspin of Adam Zampa.
Both the seamer and spinner would play their part in the defence of 270, but it was Marsh who struck the vital blows after Hazlewood had ended a firm opening stand between Andre Fletcher and Charles.
Mixing cross-seam deliveries with his usual seam-up offerings and the occasional bouncer, Marsh took control of proceedings in a manner Langer would have been particularly proud about.
Bravo was cramped from around the wicket and edged behind, Samuels was flummoxed by a ball that stopped in the wicket and gifted a front edge to short cover, and then Charles was struck in front of the stumps by a quicker delivery.
From 72 for 4 in the 21st over there was only the narrowest path back into the match, and for all the efforts of Denesh Ramdin, Kieron Pollard and Holder, Australia always had too much of a scoreboard edge. Their victory was a worthwhile moment for a young team who overcame some unfamiliar conditions and injury to David Warner to vindicate their No. 1 spot on the ICC's ODI rankings.
Khawaja and Finch had made a smooth start against the new ball, finding the boundary regularly and motoring along at better than five per over. It was something of a surprise when Khawaja tried a flat-footed forcing shot at Holder and edged behind, but even so Finch's momentum was barely stopped by the wicket.
Instead it took the arrival of Kieron Pollard to draw a miscue, a slower cutter dragged from outside off stump and taken at deep midwicket to deny Finch a half-century. Smith and Bailey prospered for 51 runs, consolidating the innings for further acceleration, but the Tasmanian lost the thread when he tried to run Carlos Brathwaite behind point and dragged onto the stumps.
Smith had played a deliberate innings, not taking undue risks, and one of his first gambles resulted in his downfall when a pull from Gabriel skewed straight up. Next man Maxwell did not suggest permanence in his brief stay, and the innings had turned when Gabriel pinned him in front.
Marsh added to the procession when he edged Sulieman Benn onto the stumps, leaving Wade to fight for a competitive tally with a series of muscular tugs over the leg-side field. He did so after surviving the wiles of Sunil Narine, a consistent source of trouble for Wade in the past, and finished the innings by clouting a Brathwaite full-toss for six.
Those late blows made a psychological difference to proceedings, before Marsh whirred down the spell that dictated the course of the match and, in turn, the triangular series.
Daniel Brettig is an assistant editor at ESPNcricinfo. @danbrettig