Chasing a first series win on these shores since 2001, touring captain Tim Paine made the surprise decision to send England in at one of the truest tracks on the circuit.
The gambit might have paid off had their fielding been better but Root saw regulation chances put down on 24, 25 and 30 before taking tea unbeaten on 51 alongside Jonny Bairstow.
Peter Siddle, wicketkeeper Paine and star batsman Steve Smith were the guilty parties, but loose shots from Joe Denly and Ben Stokes kept the bowling side interested after Rory Burns made 47 at opener.
Top-order batting has been a fiendishly difficult endeavour this summer and Pat Cummins beat Burns' outside edge twice in the first over of the day.
The Surrey captain was given out lbw for four as Josh Hazlewood kept the pressure up from the other end but Burns immediately referred the decision and was reprieved on height.
Things were no easier for Denly, who twice felt bat on ball after attempting to leave and picked up a couple of lucky boundaries while not in full control.
Cummins struck in the ninth over, tempting Denly (14) outside off stump and leaving Smith to hold a juggled chance at second slip.
Remarkably, by putting on just 27 the England openers had just put on the biggest first-wicket partnership of the series. Whether that is enough to extend Denly's international career remains to be seen, but in averaging just under 25 he has hardly made a watertight case.
Siddle offered Root a soft start to his innings, with the 34-year-old shipping 18 runs in three overs of very gentle seam bowling and, with Burns settling well, the wisdom of Paine's decision was starting to seem dubious.
Australia had the chance to reset the tone when Root top-edged a pull off the ever-impressive Cummins, leaving Siddle a simple take at fine leg. Somehow the veteran allowed the ball to slip through his grasp.
If dropping the opposition's best batsman once is a mistake, doing so twice is a sin. And so it was when Root, having added just a single to his score, sent a edge to first slip.
Paine decided to leap in front of David Warner and go one-handed but the ball bounced out of his glove and Burns was able to shepherd the score to 86 for one at lunch.
Australia's profligacy in the field unbelievably continued in the first over of the afternoon session, Siddle this time the victim rather than the perpetrator.
He tempted Root into flashing away from his body and, yet again, he turned to see the ball hit the deck – Smith the latest to fumble.
Root was riding his luck but making hard work of it, with 14 runs in the first hour before he passed 50 for the fourth time in the series.
Burns was three runs away from his half-century when Hazlewood dug one in on a leg-stump line, forcing the left-hander into a reflexive act of self defence. The ball looped up, leaving Marsh to stroll in from mid-on and gather.
Stokes was in at number four, up a place in the order following Jason Roy's omission, but he never got going. After hustling to a scratchy 20 he took on a short ball from Marsh, sending a thick edge spiralling off toe to Nathan Lyon at point.
Bairstow then picked up the rate, taking some of the pressure off Root before the interval.