Root survived a close lbw shout on 11, the decision going with umpire's call on review, and nearly chopped on to his own stumps during 12 increasingly tense deliveries on 99 not out.
The 33-year-old moved to three figures in his 145th test with a trademark four through third man to equal former England opener Alastair Cook's tally of test centuries.
Root and Gus Atkinson compiled a seventh-wicket partnership of 92 against a tiring Sri Lanka, before Root fell for 143 with a scuffed scoop off Milan Rathnayake.
Atkinson (74 not out) and Matthew Potts (20 not out) then saw off eight overs of the second new ball with aplomb and Sri Lanka will want to wrap up the tail quickly and utilise good batting conditions.
Root played down his England record-equalling century and said his desire to keep playing was undiminished.
"I remember walking out of my first test thinking if this is my one and only opportunity to play for England then I'd be extremely proud," he told reporters.
"So nice to be sat here today having achieved what I've achieved, but I feel there's still quite a lot more to do – and within this game as well."
Root said his celebration when he reached his century was a tribute to former England batsman and coach Graham Thorpe, who died this month aged 55.
"Thorpey was one of those people that offered me so much and it was nice to be able to think of him in that moment," he said.
Sri Lanka captain Dhananjaya de Silva's surprise choice to bowl under glorious sunshine at the toss was initially vindicated by early wickets.
When Ben Duckett hit three quick boundaries, De Silva – who opted to bat at Old Trafford last week, only to see his side fall to 6-3 – may have had second thoughts.
But England lost Dan Lawrence, Ollie Pope and the well-set Duckett cheaply as the hosts reached 97-3 at lunch.
Lawrence (9) edged Lahiru Kumara to keeper Nishan Madushka before England's stand-in captain Pope (1) top-edged a swipe off Asitha Fernando to give De Silva a simple catch.
Root clipped his first delivery for four, but the impressive Kumara beat his outside edge and then rapped him on the pad, with Root saved by the on-field decision.
England otherwise appeared comfortable until Duckett (40) mis-hit a reverse sweep in spinner Prabath Jayasuriya's first over to Kumara at deep point.
Harry Brook (33) scored with relative ease after lunch but Fernando trapped him lbw, the review going Sri Lanka's way on umpire's call this time, as England slipped to 130-4.
Sri Lanka initially kept Jamie Smith quiet before he and Root moved through the gears in a partnership of 62, which ended when Smith (21) nicked Rathnayake behind to Madushka.
Chris Woakes (6) fell to Kumara shortly after, caught in the deep by Fernando, to bring Atkinson to the crease with England 216-6 and Sri Lanka well on top.
Atkinson justified his place at No. 8 as he brought up his first test fifty with a glorious cover drive for four off Rathnayake in an assured innings featuring four sixes.
Root's late dismissal means Sri Lanka may feel they shaded the day on a docile surface, but they will need to bat well to capitalise.
--Reuters--