Root piled on 228 in last week's series opener at the same ground and continued to dominate the home attack as he reached three figures in consecutive matches for the first time in his career.
At lunch on day three Root was making merry on 105 not out but his near flawless innings could not disguise the fact that Sri Lanka still had a strong platform to work from. At 181 for four, England remained exactly 200 short of parity.
Lasith Embuldeniya, who removed both openers cheaply on Saturday evening, was the primary threat and made another double strike in his first spell as Jonny Bairstow and Dan Lawrence were undone by his left-arm spin.
Responding to Sri Lanka's 381, Root and Bairstow took their steady third-wicket stand from 93 to 111.
Bairstow had chipped in just 28 of those and, with wicketkeeper Niroshan Dickwella reminding him at regular intervals that he had been 'dropped' rather than rested for the forthcoming India series, he nicked an inside edge on to his front pad and was caught at slip.
Root had resumed on 67 and immediately began accumulating again, rocking on his heels to pull Embuldeniya for four and getting stuck into his trusted arsenal of sweeps.
He was getting better with each passing moment, not least when he took the chance to show off a remarkable switch hit – flipping his stance in the style of Kevin Pietersen and striking for four in the manner of a left-hander.
He was making things look easier than they were though, with new man Lawrence surviving a stumping chance before becoming Embuldeniya's fourth victim. Like Zak Crawley before him, Lawrence was drawn in by the drift and beaten by the spin, nicking to slip for three.
Root brought up a brilliant century off 139 balls – 24 quicker than his first hundred last time out – joining another Yorkshire great, Sir Len Hutton, on 19 Test tons.
Jos Buttler made a bright 30no as England continued chipping away at their hosts, hitting one sweet drive and a couple of neat reverse sweeps.
He was given out to Dilruwan Perera on 26 but a DRS review showed an inside edge into the ground which scotched hopes of an lbw or a catch.