After being sent in to bat at Karen Rolton Oval on Sunday, the Tigers broke the competition record for largest total, with captain Jordan Silk contributing 116 runs of their 9-435.
Tasmania's effort was 15 runs greater than the 420 South Australia managed against the Cricket Australia XI in 2016.
But a hot start from Fraser-McGurk put the Redbacks in position to make history themselves.
Despite never having scored a century in any form before Sunday, he needed only 29 balls to reach triple figures, two fewer than South African great AB de Villiers in an ODI in 2015.
The next-fastest ton by an Australian in a domestic one-day match, scored by Luke Ronchi, was 22 deliveries slower.
In total, the 21-year-old smacked 23 boundaries, 13 of which were sixes. Prior to Sunday, he had only hit 18 sixes in the 49 games of his professional career.
Fraser-McGurk's formidable innings finally came to an end when he hit Beau Webster's off-spin to mid-wicket and was caught by Jake Weatherald.
Without him, the Redbacks were never able to fully take advantage of the flat Adelaide deck.
All-rounder Mitchell Owen was the pick of the bowlers for Tasmania, taking 3-46 including Daniel Drew (52) and Jake Lehmann (35) before they could truly kick on.
The Redbacks were all out for 398 in the 47th over, which was still the fifth-highest total in Marsh Cup history and the largest one not to win.
Earlier, Silk helped steady Tasmania's ship after the loss of openers Caleb Jewell (90) and Jake Weatherald (35) in the space of two overs.
On a day of carnage, the 31-year-old showed his maturity by moving slowly through the nervous 90s before launching into party mode after passing triple figures.
His innings came to a halt in the 45th over, when he attempted to slog McAndrew for a 15th boundary but was caught by Ben Manenti at deep midwicket.
Silk's century was his first in 57 List A matches.
The result comes after the Tigers dropped their first two games and sat bottom of the ladder and leaves the Redbacks chasing their first 50-over win of the summer.
