Root, by reaching 23 when he punched Mohammed Siraj through the offside for his fifth four, surpassed retired former captain Alastair Cook's record of 15,737 runs in 257 matches across all formats for England.
It took India just five balls to reduce England to none for one, with left-hander Rory Burns lbw to a Jasprit Bumrah delivery that cut back in.
Crawley had been largely untroubled until the 21st over. He survived a review for lbw and caught behind, with replays showing the ball had missed the inside edge by a distance.
Root, however, square-drove Ravindra Jadeja's left-arm spin for four and struck a similar boundary off Shardul Thakur.
India dropped off-spinner Ravichandran Ashwin and fast bowler Ishant Sharma after they had both featured in a World Test Championship final loss to New Zealand at Southampton in June.