Chasing history as just the second team to come back from 2-0 down to win a five-Test series, England need Root to repeat Don Bradman's heroics in 1936-37 to save the series.
Bradman scored 270, 212 and 169 in Australia's revival.
"I expect a response from our players and I would like to bring a nice Christmas present home for everyone who stays up," Root said.
"I feel in a really good place with my batting. I feel confident I can, in these next three games, bang out a hundred in these conditions.
"I know that's a brave thing to say but my conversion rate, this year, it's not been an issue at all.
"I feel like I have managed that well and have an understanding of how I want to score my runs.
"There's clarity there, I just need to keep putting myself in those positions, just have the bit between my teeth, (make it) 'over my dead body'."
Root has enjoyed a record-breaking 2021, with his haul of 1,630 Test runs placing him in uncharted territory among Englishmen and fourth on the all-time list over a calendar year.
He has scored six centuries in that time, but scores of 89 and 62 in the first two Tests mean he now has eight unconverted 50s on Australian soil.
Boxing Day would be the perfect stage, and Root could also have the added bonus of reclaiming the world No.1 spot from Australian counterpart Marnus Labuschagne, who leapfrogged him last week.
"I've never been one for that stuff, but it would be nice to have it back for Christmas," he said with a smile.
England are expected to make at least three changes with Zak Crawley likely to open in place of Rory Burns, while Ollie Pope and Chris Woakes could be replaced by Jonny Bairstow and Mark Wood.
A fourth change could come if the pitch is judged to suit spinner Jack Leach, while Jos Buttler is expected to lose the gloves but stay in the XI after his fighting fourth-innings knock in Adelaide.
It comes after Root helped lead a honesty session following the 275-run loss.
"I'll always try to look at things with a level, pragmatic approach but I don't think you could after the way we've played those last two games," Root said.
"I expect a response from everyone this week. I just hope it's not too late."
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