The hosts lost three wickets for 13 runs, after a century stand between Alastair Cook (79) and Gary Ballance (64). But as at Old Trafford last week, Root (92 not out) and Jos Buttler (45) restated England's authority as they closed on 385 for seven, giving them a lead of 237.
Root's 93-ball half-century was his fifth of the series. He has scored one in each match to replicate a feat achieved previously by only two Englishmen, although a third, John Edrich, made it six in six in Australia 43 years ago. Ballance had lavish praise for his fellow Yorkshire batsman, and also pointed out that England of the recent past might have gone into terminal decline once wickets began to tumble.
"It was a bit of a wobble, a bit of a collapse, which is not ideal," he said. "Early on in the summer, it could have been an eight or nine-wicket collapse but it was only four. They bowled well at us and got a few wickets but the way Rooty and Jos counter-attacked was brilliant and really put us in a strong position."
Barring a major recovery of the tourists' composure after two successive defeats already, England ought to convert their mid-match advantage into a 3-1 series win and Root has once again played a significant part. The 23-year-old Yorkshireman's innings was a trademark contribution, full of his habitual hurry and scurry, with just two boundaries on the way to 50 but also a rare Root six when he hooked Bhuvneshwar Kumar towards the home dressing-room.
Cook's century drought had earlier extended to 31 innings, and the prolific Ballance could not convert his sixth 50 in 11 attempts into a fourth hundred this summer as England hit a temporary blip.
The duo fell in quick succession after putting on 125 for the second wicket. Ian Bell (seven) was soon gone too, and a fretful stay by Moeen Ali (14) ended before tea to put the onus on Root and Buttler again.
Buttler appeared set to make it three consecutive 50s at the start of his Test career, but fell short when he clipped Ishant Sharma to midwicket. By then, though, the sixth-wicket pair's Old Trafford reprise had realised 80.
Before they took over, Cook had contributed a curious innings. He was solid before lunch, yet returned almost as if the opportunity to at last make his 26th Test century had become so obvious that he could barely locate the middle of the bat.
He was twice missed badly at slip, on 65 and 70, but could not take advantage and by the time Murali Vijay made up for his earlier drop by holding a low chance off Varun Aaron it felt like a mercy as the England captain trooped off.
Ballance, who had convinced throughout and reached his 50 with an upper-cut off Kumar for his 11th four, went in bizarre circumstances, poking an innocuous length ball from Ravi Ashwin straight and slowly to silly point off the face of the bat.
When Bell then went cheaply, suddenly Root and Moeen were brought together without a run between them.
On a sunny morning, the hosts had lost only Cook's opening partner Sam Robson with just four added to their partnership, when he missed just a hint of swing from Aaron and lost his off-stump.
But Ballance was off the mark with a four first ball and had five boundaries in his first 21 runs, including three off his pads when the Indian seamers strayed there.
He appeared untroubled until his sudden aberration, after which Bell edged a good delivery from Ishant behind to Mahendra Singh Dhoni.
Moeen impressed and alarmed in near equal measure, with sweet timing but much uncertainty against Ashwin before trying to leave the off-spinner and instead edging down into his crease and on to the stumps.
Buttler's eventual departure was followed by another, Chris Woakes edging Kumar behind down the leg-side for a duck. But Root remained to milk runs off a tiring attack in an unbroken stand of 67 in just 10 overs with Chris Jordan, consolidating a position from which England should surely ease to a third successive win at some point over the next three days.