Ex-Test batsman Marsh stood tall as wickets fell around him, stroking a chanceless 101 not out to steady a wobbly WA and guide them to 6-210 in the 48th over, sealing their 14th domestic one-day crown.
Marsh showed steely resolve in his three-hour, 132-ball knock that featured 13 fours, marking his ninth one-day ton for WA.
Marsh launched his rescue mission with a 97-run fourth wicket stand with Marcus Stoinis (37) before icing the result in an unbeaten 59-run partnership with Ashton Agar (29 not out) following some anxious moments for the visitors at Allan Border Field.
Set what looked like a paltry victory target of 206, WA made a disastrous start when they slumped to 3-23 in the seventh over.
Bulls quick Michael Neser (2-34) looked dangerous as fellow Test squad member Cameron Bancroft (eight), D'Arcy Short (five) and WA captain Ashton Turner (three) all came and went in quick succession.
But Marsh and Stoinis threatened to snatch the game away from Queensland in an ominous counter attack.
They first consolidated then began punishing a Bulls attack that appeared to have dropped their heads.
Bulls captain Usman Khawaja rolled the dice and threw specialist batsman Matthew Renshaw the ball - with surprising results.
Stoinis looked set to help himself to a fourth six of his innings, only to thrash Renshaw's half-tracker to Sam Heazlett on the boundary.
Next over Renshaw snaffled up a sharp slips chance to snare Hilton Cartwright (five) and WA had gone from 3-120 to 5-133.
Marsh could only look on from the other end as it got worse for the visitors when they were reduced to 6-151 after all-rounder Cameron Green fell for seven in the 35th over.
But Marsh and Agar held their nerve to ensure WA clinched their second domestic one-day title in three years.
Earlier, Jhye Richardson (3-35 off 10 overs) and Nathan Coulter-Nile (3-47) ripped through Queensland's top order - including the prized scalp of Khawaja - after WA won the toss.
The Bulls were bowled out for 205 in the 50th over after a fighting 79 from wicketkeeper James Peirson.