Vaughan praised Finch's rotation of bowlers and brave decision-making.
Taking to BBC, Vaughan said, "I have to say Aaron Finch, so far in this tournament (World Cup), is the best captain tactically."
"I think he maneuvered his team against the West Indies well to win that game. And just over the last hour (against Pakistan), when it started to get a little bit panicky for Australia, he maneuvered his bowling attack, knowing that he had to get these overs of spin [in]," the former English captain added.
In the match, Pakistan needed 44 runs to win from 35 balls with three wickets in hand. At that time captain Finch brought his key bowler Mitchell Starc.
Starc produced two breakthroughs by removing Wahab Riaz (45) and Mohammad Amir (0) in the 45th over to give Australia the upper hand.
With just four leading fast bowlers to choose from along with all-rounder Glenn Maxwell, Finch was even forced to bowl two overs of spin himself during the innings, a move that produced the key wicket of Mohammad Hafeez, just the fourth of his ODI career.
"He got a lot of things right in the field, in terms of squeezing at the right time, putting the catchers in at the right time and then spreading them out when a partnership started to develop. I thought he was outstanding as a captain," Michael Vaughan added.