His innings was the third highest T20 ever, including domestic cricket, behind only knocks from Chris Gayle (175no) and McCullum (158no) in the Indian Premier League.
Finch's display propelled Australia to the second highest team score in T20 internationals, behind Sri Lanka's 6-260 against Kenya in Johannesburg in 2007.
In response, England managed an admirable 6-209, their second-highest T20 score, with Test opener Joe Root blasting an unbeaten 90 off 49 balls.
Playing in only his sixth T20 international, Melbourne Renegade star Finch set the tone early with a huge pulled six off his first ball.
Opening alongside David Warner (1) with Shane Watson brought in at No.4, Finch also stylishly brought up his his 50, 100 and 150 with sixes.
Finch's ton off 47 balls was the second-quickest in international T20s behind South African Richard Levi (45) and he looked poised to break that record before a brief lull in his scoring.
He was eventually clean bowled by Jade Dernbach before earning a standing ovation from the pro-England crowd.
Finch received handy support from Watson (37 off 16) and first-drop Shaun Marsh (28 off 21) but it was essentially a one-man show.
Leg-spinner Ahmed had little impact with the ball from four overs but it was hard to read too much into his debut on a batsman's pitch and with England throwing caution to the wind chasing a mammoth total.
Mitchell Johnson (2-41) and Josh Hazlewood (2-43) took early wickets to set England back even further in their chase but in truth the match was virtually won before the second innings started.
England captain Stuart Broad won the toss and may well lose sleep over his decision to send Australia to bat first on a firm Rose Bowl pitch.
Dernbach took 3-34 as most of England's youthful bowling line-up copped heavy punishment.
Of the victorious Ashes squad, only Broad and Root featured for England.
Now a fresh-faced squad faces a huge challenge to rebound in the second T20 in Durham on Saturday, which precedes a five-match one-day series.
Aside from Finch's knock, there were some other entertaining moments for the capacity crowd.
Root had a ball wedged in the front of his helmet after a short ball from Hazlewood while Ravi Bopara (45 off 28) earned a reprieve after the bails bizarrely took several seconds to fall after David Warner had brushed the wickets with a run-out attempt.
Australia had not won a match in any format since beating the West Indies in a one-day match at the MCG on February 10.
-AAP
