Root's timely, enterprising ton occupied just 120 balls and came up shortly after the tourists reached 259 for six at tea. In defying a quartet of spinners in helpful conditions and giving the innings its much-needed focal point, the captain secured the makings of a match-winning advantage.
Root's 15th hundred, just four of which have come overseas, contained eight fours and two sixes.
All six of the wickets to fall came from reverse or conventional sweeps but so too did many of England's best scoring shots. There was an admirable bloody-mindedness in watching batsman after batsman commit to the plan, unbowed by the possible consequences.
Root aside, England owed much to Rory Burns. The opener's maiden half-century set the tone for much of what followed, banishing expectations that England would be embattled passengers on a spiteful surface and turning the heat back on Sri Lanka's spinners.
Resuming with a 46-run deficit to clear, England lost nightwatchman Jack Leach in the second over of the day, leg before to Dilruwan Perera attempting a stroke far beyond his means.
What followed was a positively serene stand of 73 between Burns and Keaton Jennings, though the latter would have breathed a sigh of relief at the curious decision not to test his frailties against seam.
There was a sweet reverse sweep from Jennings to get things going and a flurry of acceleration from Burns when he struck three boundaries in nine balls, but their partnership was mostly built around smart placement and astute running.
In place of the anticipated crawl this was almost a canter, with the arrears wiped out inside 12 overs. England had nudged in front by 31 when Jennings' favourite stroke let him down, a reverse sweep edged into his body and on to the waiting slip.
His was the first in a sequence of three wickets for 32 runs. Burns and Ben Stokes both paid the price for failing to connect with sweeps against straightening deliveries and both appealed in vain via DRS.
The key difference saw Burns depart boosted in confidence by a zippy 59, an innings which did plenty to advance his Test credentials, while Stokes left with a two-ball duck.
The match was finely poised at 131 for four at lunch, with Root making his move in the first hour of the afternoon session. In that time he scored exactly 50 in 50 balls, forcing opposite number Suranga Lakmal into some defensive field placings before punching holes in them.
His confidence peaked when he savaged a length ball from Perera, clattering him for six on the leg side despite the presence of two boundary catchers.
He added 74 with Jos Buttler, England's best stand of the match, before the latter paid the price for refusing to bail out on a premeditated reverse sweep. As Akila Dananjaya ripped one off the pitch, Buttler's ungainly stretch simply guided the ball into his stumps.
Moeen Ali was wrongly given lbw for 10 but, with Ben Foakes for company, Root reached three figures with a controlled edge to third man.