In the process of their dominant triumph, the hosts have extended their perfect record at the Gabba to 31 Tests at the venue without a loss.
Pakistan began the day at three down for 64 while still needing a mountain of runs to erase the first-innings deficit and make Australia bat again.
A much-improved batting performance from the visitors saw Babar amass a glorious century - his first on Australian shores - and Mohammad Rizwan fell just five runs short of registering his maiden ton in the format.
Lower-order resistance from Yasir Shah proved to be a thorn for Australia's bowling but they eventually dismissed the tourists for 335, sealing an emphatic win inside four days and gaining 60 valuable points in the World Test Championship.
Although the margin of victory reflects a cakewalk for the Aussies, Pakistan undeniably seemed in control of the proceedings during some moments of the day.
The Australia pacers, nevertheless, stuck to their task and effectively whittled away at any progress made by Pakistan.
Josh Hazlewood reaped rewards for ratcheting up the pressure on Pakistan's batsmen by maintaining tight lines as he returned exceptional figures of 4-63.
He was aided by Mitchell Starc's fiery bowling, who took 3-73 including the last wicket to fall while Pat Cummins and Nathan Lyon shared the remaining three wickets between them.
Pakistan's premier batsman Babar Azam set up a sublime display of immaculate strokes to reach the second Test century of his career.
A lot was expected from the elegant right-hander given his outstanding form in the lead-up games but Babar perished off an ordinary cover drive in the first innings for just one.
The chanceless knock adorned by chic shots on day four offered a sharp contrast to the youngster's four-ball stay at the crease in the first innings, rendering the latter a rather distant memory.
Babar stitched vital partnerships of 68 with opener Shan Masood and 132 with wicketkeeper Rizwan before bringing up his century in style with an authoritative drive.
The 25-year-old let out a powerful celebratory roar after breaching the three-figure mark indicating how much this meant to him.
A lapse in concentration and uneven bounce in the surface soon led to his dismissal for a 173-ball 104 off Nathan Lyon as Tim Paine held onto a good catch behind the stumps.
Rizwan then followed in Babar's footsteps by taking the attack to the Australian bowlers with terrific strokeplay.
Making a comeback to the Test unit after three years, Rizwan connected his shots sweetly amidst his boundary-laden innings.
He batted with great fervour and looked all set to make his first Test ton before guiding the ball straight to Lyon at third man while trying to attempt an upper cut to clear the boundary.
Yasir kept scoring at a brisk rate and racked up a career-best 42 off 55 balls till he got out to an ill-timed flick off Hazlewood.
Earlier in the day, Masood showed immense resolve to withstand Australia's quicks and exhibited admirable application to get through the first hour unperturbed.
He ultimately faltered to a short ball from Cummins giving the home side their first breakthrough of the day.