Root, who completed his 19th Test ton in 99 matches before lunch, kept pushing in the marathon knock of 309 balls.
Bairstow, who added just four more to his overnight 24, was given not out by the umpire but Sri Lanka successfully reviewed the call as replays suggested the ball had grazed the bat before hitting the pad and being caught second slip.
The series resumed on January 14 behind closed doors after being cancelled in March due to the coronavirus pandemic.