Marsh continued the excellent form he displayed during the Indian Premier League, where he was the leading run scorer, striking seven fours and a six in his 97-ball innings.
Brad Haddin (50) and Michael Hussey (44) also added a valuable 91-run stand for the fifth wicket, after a mid-innings stumble, to help post 273 for eight.
In reply the Windies lost three early wickets to set them on the back foot and they never fully recovered in the face of some tight bowling to be bowled out for 189 from 39.5 overs.
The victory for Australia, who wore pink ribbons in memory of former player Glenn McGrath's wife, Jane, who lost her long battle with breast cancer on the weekend, lifts the reigning three-time world champions above South Africa at the top of the ICC's ODI rankings.
Brett Lee made the first of three early breakthroughs when Xavier Marshall, who sat out the majority of the Australian innings after injuring his shoulder making a diving save, thick-edged a rising delivery to Haddin when on six.
Skipper Chris Gayle (20) soon followed him back to the pavilion when Nathan Bracken trapped him leg before wicket and two balls later Lee had Ramnaresh Sarwan (two) caught by Hussey at slip.
That left the Windies 29 for three and facing an uphill task.
Dwayne Bravo and debutant Andre Fletcher steadied the ship with a stand of 51, however, it came in slow time as the Australian bowlers maintained a tight line. Bravo eventually succumbed to the tourists' accuracy when he was out lbw to Michael Clarke for 33.
Fletcher (26) then carelessly departed when he failed to recover his ground after defending a Cameron White delivery, allowing wicketkeeper Haddin enough time to pick up the ball and run him out with a neat piece of work.
The wickets continued to fall at regular intervals as the Windies never looked like keeping up with the required rate on a slow wicket at Arnos Vale.
Bracken, who was making his return following knee surgery in March, claimed the final wicket when Sulieman Benn (seven) was caught at long-on by Clarke. Bracken claimed match-best figures of four for 31.
Earlier, Marsh and Shane Watson, who was also making a comeback to international cricket after being out since last year's World Cup, put on 75 for the first wicket before the Queenslander was caught lbw shuffling across the crease by Bravo for a breezy 31 from 27 balls.
Captain Ricky Ponting (six from 20 balls) and his deputy Clarke (nine from 23 balls) fell cheaply trying to engineer shots.
Ponting chased a wide ball from Jerome Taylor only to chop onto his stumps, before Clarke got his angles wrong, gliding a Darren Sammy delivery straight to Denesh Ramdin behind the stumps.
Marsh became just the eighth Australian to bring up 50 on debut when he crunched Bravo through the covers, a shot only bettered by a glorious pull over the square leg boundary from the same bowler earlier in his innings.
But when Marsh was fooled into offering a simple catch to Gayle at cover from a Sammy slower ball the Australians looked in some trouble at 140 for four.
Hussey led the recovery mission in a risk-free 91-run stand with Haddin.
Haddin deservedly reached his half-century from as many balls before he was caught in the deep by Kieron Pollard off the bowling of Benn.
Hussey then fell to the same combination following a patient 58-ball innings, that contained just one boundary, as he looked to up the tempo.
Lee (12 not out) provided the late fireworks, including a hefty six over midwicket, to cap a solid batting display.
The second game in the five-match series will be played at St George's in Grenada on Friday.
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