After three days of Australian dominance, Root took up the challenge of a record run chase with a fighting unbeaten half-century as the momentum began to shift towards England, roared on by their bellowing Barmy Army supporters.
In contrast, his counterpart Steve Smith, who attracted criticism for not enforcing the follow-on despite a 215-run first innings lead, burned two reviews in the space of three balls and put down a tough catch.
At the close of an absorbing fourth day in the first day-night Ashes Test, England were 176 for four with Root unconquered on 67 and nightwatchman Chris Woakes not out on five -- 178 runs from victory with six wickets in hand heading into Wednesday's final day.
"A win would be huge for us, both in terms of what it would do for our confidence as a team and we would be all square in the series," England paceman James Anderson said.
"It would also have a potential effect on them (Australia) for a team to be in such a commanding position to then lose that," he added.
"It's very rare that a team declares and loses a game so if we can get a result tomorrow it would be huge for a number of reasons."
Root had a leg before wicket decision on 32 off Nathan Lyon overturned on review, with the 'Hawk-Eye' tracker indicating the ball would have gone over the stumps.
Australia then lost their second and last review in the 43rd over when Dawid Malan survived an lbw challenge on three off Josh Hazlewood, with the ball again tracked as going over the stumps.
Adding to Smith's anxiety, he also dropped Malan on eight in a sharp one-handed attempted catch at slip off Lyon.
"We're still reasonably confident," the Australia team bowling coach David Saker told reporters.
"Obviously, the last two days haven't gone to plan ... we're still in front of the game but it's getting closer and closer and Joe's innings has made that possible," he added.
"But if we can get his wicket in the morning I think the game changes quite quickly."
After the chaos of the previous night's session when Australia lost four wickets, England had a much better time under the lights. They only lost the wickets of James Vince and Malan and otherwise scored freely.
Vince was beaten by a pitched-up Mitchell Starc delivery, getting a big nick to Peter Handscomb at slip for 15. Malan put on 78 with Root before he was bowled by Pat Cummins for 29.
England lost openers Alastair Cook and Mark Stoneman before the dinner break.
Lyon won a successful lbw review to remove Cook (16), ending a 53-run opening stand with Stoneman, who was snapped up in the gully for 36.
The Australians were knocked over for 138 off 58 overs at tea but, bolstered by their 215-run innings lead, this left England with a record chase.
England's all-time leading wicket-taker Anderson took five for 43 -- his first five-wicket haul in Australia -- while fellow paceman Woakes captured four for 36.
Usman Khawaja and Starc were joint top scorers with just 20 each in Australia's modest second innings.
England kept the Australians under pressure after they resumed the day at 53 for four.
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