Australia had defeated the Green Brigade 2-0 in the three-match T20I rubber before whitewashing them 2-0 in the Test series.
After the result, Vaughan took to Twitter and wrote: "This Australian Team in these conditions are going to take some beating ... Only India have the tools to do so at this stage... #AUSvPAK."
Veteran off-spinner Nathan Lyon picked up a five-wicket haul as Australia defeated Pakistan by an innings and 48 runs in the second and final Test of the two-match series on Monday.
With the win, the Aussies clinched the two-match series 2-0 and increased their victory tally in Day/Night Tests to 6-0.
Speaking after the match, Aussie skipper Tim Paine said: "Really happy. Barring few slip-ups in the field yesterday, we played excellent cricket over the last two matches. We came back from England, we felt, we were getting better all the time.
We wanted our batters to score big runs, when your six seven and eight are not facing lot of balls then your top-order is doing fine. David (Warner) and Marnus (Labuschagne) have been unbelievably good."