Finch held his nerve in a tense finish, hitting Doug Bracewell for six off the fourth ball of the final over, after the Australian side found themselves needing 48 off the last four overs.
Finch found a solid partner in Andrew McDonald, who hit 18 not out in an unbeaten stand of 66.
"We nearly left it a bit too late, but we got over the line," said Finch, who made his runs off 60 balls with 11 fours and three sixes.
Stags captain Jamie How earlier hit an unbeaten 77 off 55 balls as the New Zealand team reached 165 for five in their 20 overs.
The Stags made a poor start, with Victoria fast bowler Peter Siddle taking two wickets in the first over.
At the halfway stage they had labored to 48 for three.
But the tournament pattern of teams struggling against the new ball and then scoring freely later in the innings continued.
How and George Worker (29) put on 53 in 48 balls for the fourth wicket before Brendon Diaminti helped How add 66 off 29 balls for the fifth wicket, which included 28 runs off the18th over, bowled by John Hastings.
Finch played a fine innings but made a lucky start. He was caught off a no-ball bowled by Bracewell before he had scored and was dropped on 43 when he hit a hard return chance to left-arm slow bowler Worker. It was one of three catches put down by the Stags.
How said his side's fielding was a disappointment.
"We had a few dropped catches and a few misfields and you can't afford to do that against a quality side like Victoria," he explained.
also in Centurion, Suresh Raina and Murali Vijay have smashed around Wayamba Elevens for Chennai Super Kings to rack 200-3 in the Champions League Twenty20 on Wednesday.
Raina joined Vijay after Matthew Hayden was out lbw for 10 at 43-1 in the sixth over, and the Indian pair plundered 137 runs in 12 overs.
Raina whacked 87 off 44 balls, including six sixes and six fours. In the over before he was out, the 17th, Raina hit spinner Ajantha Mendis four times out of SuperSport Park.
The over cost Mendis 28 runs.
Vijay hit 68 off 46 balls, with one six and nine boundaries.
Both were out off successive balls in the 18th delivered by medium pacer Chanaka Welegedara.
In Islamabad, Pakistan, Rashid Latif believes Afghanistan has the talent to achieve Test match status within two years.
Latif takes over as coach of Afghanistan this week after resigning as the Pakistan Cricket Board's wicketkeeping coach at the National Cricket Academy.
Just last month Latif resigned from a brief stay as Afghanistan's batting coach when head coach Kabir Khan was fired. Latif cited differences with Afghan officials but resolved those this week.
“I am impressed with the amount of talented players I saw in Kabul and Jalalabad,” Latif told The Associated Press on Wednesday.
“Within a year or two I hope they start playing test matches.” Latif, the former Pakistan captain, resigned from his academy job on Tuesday after making critical comments on the match-fixing scandal then explaining them to the PCB.
Afghanistan, as one of the six affiliate members of the International Cricket Council, plays one-day internationals and Twenty20 internationals but not tests. Canada, Ireland, Kenya, Netherlands and Scotland are the other five teams.
Afghanistan competed in this year's World Twenty20 in the Caribbean and impressed despite losing both of its group matches against South Africa and India.
Only the ICC can grant Test status on a team, but Latif was confident that Afghanistan was good enough now to compete in Tests with Bangladesh, ranked last of the nine Test-playing teams. Zimbabwe's Test status is suspended by the ICC but that will end next May.
“I think if they (Afghanistan) now play against Zimbabwe and Bangladesh in Test matches they can spring a few surprises,” he said.
Latif sees his primary job as preparing Afghanistan's backup players for the step up to international cricket.
“That's my main target and once it's achieved I don't see any reason why they could not compete with other test-playing countries,” he said.
