A fluent and counter-attacking Root, dropped before he had scored, hit 134 with Gary Ballance (61) and Ben Stokes (52) making solid contributions.
Josh Hazlewood and Mitchell Starc took three wickets apiece for Australia with the late dismissal of Jos Buttler leaving the game evenly poised.
England were wobbling at 43-3 when Root came to the crease on an overcast and chilly morning in the Welsh capital but he made the most of a second-ball reprieve after he was spilled by wicketkeeper Brad Haddin.
England did not lose a wicket in the afternoon session as Root prospered and Ballance scratched around to share a fourth wicket stand of 153 at Sophia Gardens, where England dug in for a memorable draw in 2009 -- the first Ashes test at the ground.
Ballance was trapped in front by Hazlewood and Starc ended Root's 166-ball stay when he induced an edge to first slip.
Ben Stokes continued the assault before Starc bowled him, the paceman celebrating with a finger-to-lips send off for the departing batsman.
Moeen Ali (26) and Stuart Broad (0) will resume on Thursday.
Root was full of aggressive intent, scoring quickly -- mixing imperious cover drives and stylish cuts -- seizing on anything short, wide or overpitched to compile his seventh test century and second against Australia.
"It's nice to make a big score so early in the series but the most important thing is we get wins. We want to win back the Ashes," Root told reporters.
"It's alright having one good day, but we have to back that up now, not just in the rest of this game but throughout the series as well. It's going to be a really interesting series."
Having lost the toss on a pitch, Australia made the most of a swinging ball as Adam Lyth (six) fell in the second over, caught low down by David Warner at gully off Hazlewood.
Off spinner Nathan Lyon, introduced in the 10th over, sent back captain Alastair Cook (20) who tried to cut him away and edged behind to Haddin. When Ian Bell's poor form continued as he was trapped leg before for one by a Starc inswinger, England were reeling.
Starc and the accurate Hazlewood caused England the most problems but there was no success for Mitchell Johnson, England's nemesis from the last Ashes when he took 37 wickets with express pace.
He got no help on Wednesday on a sluggish pitch with his 20 wicketless overs costing 87.
(Editing by Ken Ferris/Alan Baldwin)
Share
