Australia set a tough victory target of 359 — 27 runs more than any England side has managed — and reduced the hosts to 15-2, seemingly reopening the fault lines that saw the home team skittled out for a paltry 67 on Friday.
Root showed steel, determination and leadership that has been lacking in England's batsmen by sharing a third-wicket stand of 126 with Joe Denly (50) and reaching stumps unbeaten on 75. England was 156-3, still needing 203 more runs to win.
Australia leads the five-match series 1-0 and will retain the Ashes if it goes 2-0 ahead with two tests remaining. "We believe," Denly said. "If we get one or two more partnerships tomorrow, we're in with a real shout.
"I rate our chances very highly. There are not too many demons in the pitch. Their bowlers are going to get tired. The new ball will be tricky but a few of our batters are due some runs." Root arrived at the crease having failed to score in each of his last two innings — a golden duck in the drawn second test at Lord's was followed by a second-ball nought in the first innings in Leeds — but he channeled the old-fashioned virtues that his side have frequently neglected to hold firm for five hours and 189 deliveries.
His main foil was Denly, who survived an uncomfortable start to his innings to make a half-century. Root will begin Day 4 alongside his deputy, Ben Stokes, who was on 2. England's highest chase of 332-7 dates back to 1928 but Leeds has more recent history for fourth-innings drama. The West Indies hunted down 322 in 2017 and Mark Butcher led the hosts to a victory target of 315 in the 2001 Ashes.
Earlier, David Warner took his fifth catch of the match to remove Rory Burns for 7 off the bowling of Josh Hazlewood. Jason Roy was then bowled by Pat Cummins for 8, the latest failure for a batsman whose place as opener is now under threat.
Australia resumed its second innings Saturday on 171-6 and was bowled out for 246. Marnus Labuschagne, again starring in a stand-in role for the concussed Steve Smith, made 80 — one run off his highest test score — before being run out.
Jofra Archer, who took 6-45 in the first innings, claimed two of the final four wickets to end with 2-40, while Stokes had 3-56. "The wicket has flattened out a bit, we have the new ball due in eight overs which is good for us," Labuschagne said. "We have got to stick to our process, shut that scoreboard down and challenge both edges of the bat, ball in, ball out.
"If we do that, I've no doubt we will win the match."
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