Root's majestic 160 powers England to 384 in final Ashes Test
Root's superb innings was ended courtesy of a brilliant caught-and-bowled by Michael Neser, who ended with 4-60.
Will Jacks (27), Brydon Carse (1) and Josh Tongue (0) also departed in the second session at a sold-out Sydney Cricket Ground.
Harry Brook (84) and skipper Ben Stokes (0) fell to Scott Boland and Mitchell Starc respectively, while Jamie Smith (46) was dismissed by part-timer Marnus Labuschagne, all before lunch.
Australia lead the series 3-1 and have already retained the Ashes, with England desperate to keep the momentum going after clawing back a win at the previous Test in Melbourne.
Resuming at 211-3, the day belonged to Root, who started on 72 and reached an almost chanceless century off 146 balls to reaffirm his status as one of the all-time greats.
The 35-year-old began the gruelling series under pressure after failing to make a hundred in Australia over three previous Ashes tours, but he snapped the drought with a majestic unbeaten 138 in the day-night Test at Brisbane.
His exploits in Sydney drew him level with Australian Ricky Ponting to be third on the all-time century-maker list with 41.
Only India's Sachin Tendulkar (51) and South African Jacques Kallis (45) have more.
Root and Brook came together with England in trouble at 57-3 on Sunday following the demise of Ben Duckett (27), Zak Crawley (16) and Jacob Bethell (10).
Both were eyeing big centuries on a deck ideal for batting.
But Brook only lasted five balls on Monday, adding six to his overnight 78 before dabbing at a Boland delivery and edging into the safe hands of Steve Smith at slip.
It ended a 169-run partnership, not just England's best of the series but the biggest by either team, surpassing Travis Head and Alex Carey's 162 in Adelaide.
Stokes only survived 11 balls before getting the faintest of edges off Starc.
The umpire gave it not out but the decision was overturned on review and he was gone for a duck.
Jamie Smith lived dangerously and was fortunate to survive after chipping Cameron Green to Labuschagne at cover on 22. He began walking off but replays showed Green overstepped the mark.
He added another 24 before medium-pacer Labuschagne came on and bagged him in his first over, holing out to Boland.
Will Jacks slammed a six off Labuschagne in the first over after lunch but the run rate slowed significantly when the new ball was taken and Starc and Boland returned.
Root persisted, passing 150 for a 17th time, just one behind the legendary Don Bradman and three short of Tendulkar.
He and Jacks put on 52 for the seventh wicket until Jacks sent a leading edge to Green in the gully off Neser. Root then departed and the tail collapsed.