Root, who also reached 1,000 first-class runs for the season after just 12 innings when he passed 70, battled through the entire day for England before bringing up his century just after tea and ending up unbeaten on 178 at stumps.
The 22-year-old became the youngest Englishman to make an Ashes century at Lord's and, when he jogged off at the end of the day, he had put his side in complete control of the second Test.
It was a hugely impressive innings from Root, who led the hosts to a commanding 566-run second-innings lead over a dispirited Australia with his side having started the day on an unconvincing 31-3 after losing quick wickets at the end of day two.
The Yorkshireman shared an valuable 99-run partnership with county team-mate Tim Bresnan (38) before combining with Ian Bell (74) – the England centurion from the first innings – in the final session to reach his second Test century in just his seventh match.
There was a thoroughly deserved standing ovation for the opener as he moved to three figures after tea with an effort that saw England bat Australia out of contention in the second Test after the hosts won the first in thrilling fashion at Trent Bridge.
First innings century-maker Bell, who was looking to become only the fourth Englishman to reach triple figures on two occasions in an Ashes Test, fell 26 runs short after hitting a poor long hop from leg spinner Steve Smith to Chris Rogers at midwicket.
But there was controversy earlier in the day as Bell, who had made only three at the time, was very fortunate to survive after he fended a ball from Ryan Harris to gully where Smith appeared to take a clean catch.
The umpires asked for a review and, after several TV replays, decided that there was a sufficient element of doubt over whether the fielder had taken the ball cleanly as he dived forward.
The Australians were not impressed as the decision was overturned, and Harris and Smith made their feelings clear while there was some booing from spectators. It was another poor passage of play in a dramatic series as the officials continue to struggle with using the DRS.
Alastair Cook’s side assumed control from the outset as Root led the way in a subdued morning session, accompanied by nightwatchman Tim Bresnan (38), and Australia were forced to toil in the field with the pitch offering their despondent bowlers very little.
Three wickets had fallen in rapid succession to Peter Siddle late on Friday evening, but Australia’s pacemen were unable to find a breakthrough on a cool, overcast morning – in contrast to the two gloriously sunny days that preceded it.
Root brought up the third half-century of his fledgling Test career from 122 balls with six boundaries including a crisp on-drive off the first ball of the day, and he would only go on to build from that point.
Bresnan provided solid support after taking 30 deliveries to get off the mark, highlighting just how easy-paced the pitch was by playing almost exclusively off the front foot against the Australian pace bowlers.
The nightwatchman, who was brought in to replace the out-of-form Steven Finn for this Test, took England past the century mark with his fourth boundary, cracking a wide short delivery from left-arm spinner Ashton Agar backward of point before he miscued a pull shot to Rogers at midwicket off the bowling of James Pattinson.
Bell joined Root at the crease, and the in-form batsman provided his class and composure at the other end as Root reached his 100 after the tea break in what was a day of utter dominance from England.
The Warwickshire man, whose century in the first innings was his third in successive Ashes Test matches, was distraught to fall short of another ton as he holed out to Rogers with Smith left to celebrate a delivery that deserved to be hit away for a boundary.
It was then left to another of Root's Yorkshire team-mates, Jonny Bairstow (11 not out), to accompany his friend to the close of play with Cook biding his time over a declaration with two full days still remaining in what has turned out to be a hopelessly one-sided contest - in stark contrast to the dramatic finale in Nottingham.
The tourists, already one-down in the five-Test series, were crucially dismissed for a dismal 128 on day two in reply to England's first innings 361 as the tourists conceded a significant deficit, from which they have only recovered on four previous occasions in Ashes history away from home. It does not look remotely likely that Michael Clarke's side will be able to confound that statistic.
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