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Buttler hit an undefeated 77 off 54 balls in the second T20 with eight fours and two sixes, including the winning, runs off Adam Zampa.
England finished on 158-4 in 18.5 overs at an empty Rose Bowl.
Top-ranked Australia chose to bat first and lost the opener, David Warner, for a duck before recovering from 3-2 in the second over to reach 157-7.
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Dawid Malan scored 42 runs off 32 balls for England which still needed 18 runs off the last two overs.
England beat Australia by two runs in a thrilling first T20 on Friday that went down to the final ball. Chasing 163 to win, Australia collapsed from 124-1 after 14 overs.
Australia is playing international cricket for the first time in six months because of the coronavirus pandemic.
The third and final T20 is at Southampton on Tuesday.