The seventh-wicket pair took their overnight stand to 134 to help England to 325 for eight, and a lead of 173, at lunch at Emirates Old Trafford.
Both were dismissed before the interval, Root and Buttler falling for 77 and 70 respectively to become Pankaj Singh's first Test victims, but England were tightening their stranglehold.
With a poor weather forecast for Sunday, the hosts will be expected to push on in the afternoon and all but set up a victory which would put them 2-1 ahead in the series.
Despite the two wickets, it was not a distinguished morning for India or, particularly, their captain Mahendra Singh Dhoni.
Dhoni struggled to find a way to break the critical Root-Buttler stand, both tactically and with his own actions.
His most glaring error came when he failed to gather a throw from Varun Aaron cleanly and missed an opportunity to run out Buttler when he was on 44.
That was actually one of three reprieves for the fortuitous wicketkeeper-batsman Buttler, who otherwise tempered his normal aggressive game to play a controlled innings.
Buttler, playing his second Test, was dropped on 34 by Virat Kohli in the gully off the bowling of Bhuvneshwar Kumar. He later survived a marginal lbw appeal, shortly after reaching his half-century, off the same bowler.
Root was troubled less and made comfortable progress as he continued his outstanding summer.
The Yorkshire batsman reached his half-century in the second over of the morning with a clip to fine leg for three runs - sending Kumar diving through the patch of muddy outfield that prematurely ended Friday's play.
Root has now passed 50 in each of the four Tests in this series, in a season in which he also scored a double century against Sri Lanka.
The threat of India's seamers was not as strong as on the second morning, although Pankaj did beat Buttler's outside edge early on.
The new ball was taken at the earliest opportunity, in the 10th over of the morning, but Buttler took immediate advantage by cracking successive fours through the covers.
Buttler remained the more assertive partner but Root had just started to play more expansively when his demise came.
Root took the score past 300, and the lead over 150, with two crisp fours in one Aaron over but then gloved a catch down the legside to Dhoni off the hitherto luckless Pankaj.
Pankaj, after recording the worst figures by a Test debutant in the last match at Southampton, looked relieved to finally register a wicket after conceding 274 runs.
Root's innings had occupied 161 balls and contained seven boundary fours, as well as two all-run fours.
Better was to come for Pankaj as a well-disguised slower ball just before lunch lured Buttler into chipping a catch to Cheteshwar Pujara at mid-off, ending a 130-ball knock which included 10 fours.
Chris Woakes and Stuart Broad were at the crease at lunch.
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