After heavy defeats in Brisbane and Adelaide, the visitors must win in Melbourne to keep the five-Test series alive, with Australia only needing a draw to retain the urn as holders.
Labuschagne, the ninth Australian man to cross the 900-point mark in the ICC's Test batting rankings, is ahead of Root, with Australia's Steve Smith third, New Zealand captain Kane Williamson fourth and India's Rohit Sharma fifth in the latest standings published on Wednesday.
The tourists resumed in Melbourne on 31 for four, still 51 runs behind, after a disastrous final hour on Monday against some outstanding fast bowling that left their Ashes dreams in tatters.
England, set a target of 271 for victory, crashed to 124 all in the last session on the third day at Hobart, losing 10 wickets for 56 after Zak Crawley (36) and Rory Burns (26) combined in a 68-run opening stand.
Australia once again defeated England 4-0 and lifted the Ashes series on Sunday. Throughout the series the English team looked very ordinary especially in batting. None of the English batters managed to impress.
McDonald, 40, secured a four-year contract after winning praise for his performance as interim coach since Langer's abrupt resignation on February 5 shook the cricket world.
After restricting England's second innings to 297, the Australians needed just 20 runs to clinch the match. They did it in 5.1 overs, for the loss of only makeshift opener Alex Carey (9), with Marcus Harris (9 not out) hitting a boundary to finish off.
It is an even harder task at the Adelaide Oval, where Australia's 315 for six to defeat England in 1902 remains the best fourth-innings run chase. England's problems stem from being bowled out, after a batting collapse, for 236 on Saturday in reply to Australia's 473 for nine declared.
The Pakistan-born Khawaja, playing his first Test since the 2019 Ashes series in England in place of COVID-isolated Travis Head, was at his unflappable best in notching an unbeaten hundred to put Australia in charge at 321 for six at tea.