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 (2-80).
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.
"We are playing in a team that really enjoys the way we go about it so just trying to soak it up as much as you can," Root told Sky Sports. "Enjoy the journey and I am sure at the end of it all I will be able to look back on it fondly."
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 3-6 – may have had second thoughts.
But England lost Dan Lawrence (nine), Ollie Pope (one) and the well-set Duckett (40) as the hosts reached 3-97 at lunch.
Harry Brook (33) scored with relative ease after lunch but Asitha Fernando (2-84) trapped him lbw, the review going Sri Lanka's way on umpire's call this time, as England slipped to 4-130.
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 Nishan Madushka.
Chris Woakes (6) fell to Lahiru Kumara (2-75) shortly after, caught in the deep by Fernando, to bring Atkinson to the crease with England 6-216 and Sri Lanka 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.
England won the first Test of the three-match series by five wickets.
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