After captain David Warner won the toss and elected to field, the Aussies dismissed unsafe opener Jason Roy in just the second over before a few solid partnerships consolidated the innings for England.
For Australia, Maxwell remained the best bowler with 3 for 10.
The Australian all-rounder finished the match with 103 runs off just 53 balls.
However the replays appeared to give enough evidence for the third-umpire to reverse the on-field decision. After being dropped by Alex Hales on 40, Maxwell looked to have been caught on 59 by a low catch to Jason Roy at long-off. The Victorian stood up amid a stuttering Australian innings, which started disastrously at 4 for 2.
Two balls later, Chris Lynn was walking back to the pavilion for a duck after having his stumps rattled.
Fresh from his stint with the Hobart Hurricanes, D'Arcy Short was right at home at Blundstone, belting a quick-fire 30 off 20 balls, with two fours and two enormous sixes.
In-form Short (30 from 20 balls) looked set for a breakout knock at the global level but hammered a return catch to Rashid, whose wily turn was getting England back into the contest. Chasing England's total of 155/9 at the Bellerive Oval in Hobart, Australia notched up 161/5 with nine balls to spare.
The limited-overs specialist struck 103* off 58 deliveries at the Bellerive Oval - including one final authoritative six - to add to his impressive bowling figures of 3-10 and ensure that the hosts successfully chased down a target of 156 in the Twenty20 clash.
England were without four players when they tuned up for the series with a demolition job on the Prime Minister's XI in Canberra, but are looking healthier after a couple of days in Tasmania.
Australia are now atop the standings in the inaugural triangular T20 tournament after notching up a comfortable seven-wicket victory over New Zealand at the SCG on February 3. Kane Richardson drew first blood, in the second over of the match.
The Poms limped to 155 runs from their 20 overs.
Hales was the first of two caught-and-bowled dismissals for Agar, and when Morgan went, caught by Warner off Maxwell, it sparked a middle-order collapse. Malan was the only England batsman to have scored a fifty in the innings, with the second-highest scorer being 22.
Ashton Agar (2-15) reacted quickly to remove Hales caught and bowled despite having his view blocked by Malan at the non-striker's end in the seventh over, and Morgan fell top-edging Maxwell to Warner at mid-off three overs later. When Willey ran down the pitch to Maxwell and failed to repeat the blows than had taken 34 from a Nathan Lyon over in England's Canberra warm-up match, Australia were very much in control.