Green was caution itself before reaching the half century mark but then accelerated with the declaration in sight, plundering four big sixes before getting a faint edge to a Bumrah delivery.
Tailenders Starc (14 not out), Pat Cummins (22) and Hazlewood (10) showed stiffer resistance than a number of their batting team mates to push Australia to 200 for the first time in the series.
But Cummins finally got the wicket he deserved when Gill, who added 17 to his overnight score after being preferred as opener to the axed Prithvi Shaw, got a nick and Paine took a simple catch.