Australia declared their second innings on 230/9 before the tea break, setting England an improbable victory target of 468.
The touring side were 82/4 at stumps, losing Root in the final over and staring at a second successive heavy defeat in the five-match series.
Ben Stokes, whose batting heroics secured England’s most successful Ashes run chase at Leeds two years ago, was on three with his team still 386 short of their target.
Australia showed their intent by removing opener Haseeb Hameed for a duck before tea and sent back Dawid Malan, who made 20, after the break.
England settled briefly as Rory Burns, who had managed 17 runs in his three previous innings on this tour, held firm before departing for 34, caught by Steve Smith in the slips off a Jhye Richardson lifter.
Australia are six wickets away from going two-nil up in the #Ashes.
— cricket.com.au (@cricketcomau) 1639914211000
Starc floored Root with a painful blow to his abdomen before dismissing the England captain to cap another satisfying day for Australia.
Earlier, Marnus Labuschagne followed his first innings century with a fifty and Travis Head made 51 as Australia declared on 230/9 half an hour before the tea break.
England claimed three wickets in the first session but Labuschagne and Head settled any nerves in the Australia camp before stand-in captain Smith declared.
West Indies hold the record for the highest successful fourth innings chase of 418 achieved against Australia in 2003.
England’s most successful Ashes chase came at Leeds two years ago when they reached their 359-run target thanks to Stokes’s superb century.
It took 12 balls for an English wicket to fall with Richardson removing Haseeb Hameed caught behind for a duck.
Starc was treated for a back injury incurred while batting but showed no ill-effects.
Stokes temporarily took over England captaincy as Root had a hospital scan after being hit in the abdomen during Sunday’s warm-up and he limped off the field following his dismissal to complete a depressing day for his team.