Batting after skipper Ben Stokes won the toss at a sold-out Sydney Cricket Ground, Root and Brook steered the tourists to 211-3 when bad light forced them from the field just before tea.
Subsequent rain and the risk of lightning made no further play possible.
The pair came together with England tottering at 57-3 after losing Ben Duckett (27), Zak Crawley (16) and Jacob Bethell (10) before lunch.
The world’s top two-ranked batsmen set about counter-attacking on a decent batting pitch providing little movement for the bowlers, who toiled hard in the second session without joy.
Both brought up hard-fought half-centuries and, with dark storm clouds looming, kept the scoreboard ticking over at a fast clip.
England came into the game buoyed by a four-wicket win inside two days in the previous Test in Melbourne, desperate to keep the momentum going.
That victory snapped a 15-year winless streak in Australia but came too late to save the series, with the host retaining the urn by winning in Perth, Brisbane and Adelaide.
ALSO READ: When was the last time Australia played a Sydney Test without a spinner?
Australia sprang a surprise by including allrounder Beau Webster in place of quick Jhye Richardson, with off-spinner Todd Murphy overlooked.
It is the first time in almost 140 years that the hosts have not played a front-line spinner during a Sydney Test.
England brought in seamer Matthew Potts for the injured Gus Atkinson in their only change, with their frontline slow bowler Shoaib Bashir missing out for a fifth straight Test.
The day began with a tribute to first responders at the Bondi mass shooting last month that killed 15 people, with huge cheers when hero Ahmed Al Ahmed, who tackled one of the gunmen, appeared.
Duckett was lively when play started, crunching five boundaries from Mitchell Starc in a quickfire 27 off 24 balls.
But England’s tormentor-in-chief Starc had the last laugh, enticing an outside edge from an angled ball to wicketkeeper Alex Carey at full stretch.
It was the fifth time Starc has bagged Duckett this series.
Crawley was next to go, trapped lbw by Michael Neser to send both openers back in the sheds by the first drinks break and leave the tourist in trouble on 51-2.
A cautious Bethell took 15 balls to get off the mark and never looked confident.
He departed after prodding at a moving delivery from Scott Boland that took a faint edge and was collected easily by Carey as England fell to 57-3.
Root joined Brook at the crease and they began to rebuild.
They rotated the strike well and punished any loose balls with Root bringing up his 67th half-century, and the 100-partnership, with a single off Webster.
Only Indian great Sachin Tendulkar with 68 has scored more Test fifties.
Brook was fortunate to survive on 45 when he slogged Starc and the ball dropped between three chasing fielders.
But he kept his composure to reach a 15th half-century four balls after Root, cracking Webster through the covers for a boundary.
Published on Jan 04, 2026
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