In combining for a 246-run opening stand the duo set a new Australian record first-wicket partnership, eclipsing the 212 set by Shaun's father Geoff Marsh and David Boon against India in 1986.
David Warner's omission from the one-day squad allowed Marsh and Finch to rekindle their recent opening partnership for Australia A and they made it count.
QUICK SINGLE: Statement from James Sutherland
"I've really enjoyed batting with Finchy over the last few months," Marsh said.
"It's great to do it again today for Australia hopefully we can get a few more chances in this England series."
After losing the toss in the one-off match at Grange Cricket Club, Australia posted a mammoth first-innings total of 3-362.
In response, a Scottish side featuring several amateurs was bowled out for 162, with Mitchell Johnson claiming 4-36.
After impressing in Twenty20, former Pakistani refugee Fawad Ahmed bowled well on his ODI debut with 1-39 from 10 overs.
With England made to work much harder for a win over Ireland in Malahide on Tuesday, Marsh felt Australia would take plenty of momentum into Friday's series opener in Leeds.
"The boys got a good hit-out," Marsh said.
"It's just nice to spend a bit of time out in the middle and the boys bowled really well as well."
They struggled for runs early, making just 11 off the first five overs, before Finch got the scoreboard ticking over more freely.
Following on from his world record Twenty20 knock against England last week, Finch's 148 from 116 balls was his first one-day century having never made more than 38 in seven previous ODI appearances.
The 26-year-old was overlooked for the Champions Trophy but has now cemented his spot and looms as a danger man against England.
Unlike Finch's explosive T20 innings of 156 from 63 balls in Southampton last week - the highest score in T20 internationals - his innings on Tuesday was more about patience and restraint, at least early on.
He brought up his century off 96 balls and saved most of his trademark "Finch hitting" until after the milestone in an innings that featured seven sixes.
Finch was caught by Freddie Coleman off Majid Haq's bowling, falling just short of becoming the eighth Australian to score 150 in an ODI.
Marsh later achieved that feat after playing a supporting role to Finch for much of the innings.
The 30-year-old, who missed selection in the Ashes, upped the ante after Finch's dismissal and reached his third one-day century from 128 balls.
He needed only another 21 deliveries to race to 151 before being caught by Gordon Goudie off Ian Wardlaw, who also dismissed Watson (37 off 24) on the next ball.
The Scots could have capitulated after being 2-1 in response when Johnson and Clint McKay made early breakthroughs.
But contributions from Matt Machin (39), Goudie (24), Calum MacLeod (24) and Haq (24) ensured they survived until the 44th over.