Both he and Smith focused instead on swift running between the wickets and the easy ones and twos on offer.
Smith fell for 47 in the 40th over and Finch trudged off the following over as Australia slumped from 2-216 to 6-248.
"It's a perfect warm-up for the World Cup, you want to win games under pressure," Brad Haddin said after scoring an unbeaten 13 off 11 balls.
India's total of 8-267, built on the back of Rohit Sharma's masterful 138, was proven to be sub-par on a pristine batting pitch.
As a battle between the No.1 and No.2 sides on the ICC's one-day rankings, it was a decent World Cup tune-up.
As an encore to the four-Test series, in which Smith compiled an unfathomable 769 runs, it delivered some new hits.
Finch banked on patience instead of power batting, with the opener reluctant to take a risk following the dismissals of David Warner (24) and Shane Watson (41).
But Mitchell Starc, leading the pace attack in the absence of fellow left-armer Mitchell Johnson, was man of the match.
Starc finished with career-best figures of 6-43.
One run less and he would have equalled Ajit Agarkar for the best figures achieved in an ODI in Australia.
Starc struck late and early, helping reduce the visitors to 3-59 before Sharma steadied.
Sharma's knock was the highest ODI score by a visiting batsman at the MCG since Sir Viv Richards' unbeaten 153 in 1979.
He pushed India to a score of 3-185 in the 35th over alongside half-centurion Suresh Raina, when a total of more than 300 was on the cards.
Starc dismissed both men, as India managed 61 runs from their final 10 overs.
A full toss from Starc was an inappropriate end to Sharma's masterful innings, with the opener popping up a regulation catch to Maxwell at midwicket in the 49th over.
As was the case in the Test series, tempers flared.
The flashpoint came following the 23rd over of India's innings, when Sharma and David Warner came face-to-face in an ugly stoush.
Umpires John Ward and Kumar Dharmasena intervened to separate Sharma and Warner, while captain George Bailey also attempted to cool things down.
"I think Rohit was fine with it, I didn't even bother to ask what really happened," India skipper MS Dhoni said of the heated confrontation. "It was between two grown men and I hope it was sorted out in the middle."
-AAP
