Root began the day by winning his eighth toss in a row, cashing in on his remarkable luck by choosing to bat first for the third time in the series, having established a winning formula in Galle and Kandy.
The pitch at Colombo's Sinhalese Sports Club did not offer the elaborate early turn seen in those two matches but still saw Rory Burns (14) and Keaton Jennings (13) fall to Sri Lankan spinners in the first hour.
Burns appeared well set until an ill-judged back cut against Dilruwan Perera in the eighth over, stepping away and paying with his off stump. Jennings also fell softly, turning Malinda Pushpakumara's fifth delivery straight to the newly-installed leg slip.
That left England's new number three, Bairstow on recall, and captain Root to steady matters and the Yorkshire duly put on an unbeaten 66.
Both men survived DRS referrals as Sri Lanka again wasted that precious resource, a caught behind shout against Bairstow flicking elbow rather than bat while Root was hit outside the line of off stump by Lakshan Sandakan.
Bairstow was producing a persuasive audition in the problem position, driving his first ball through cover for four, taking back-to-back boundaries off Sandakan and swatting Pushpakumara for a dismissive six over midwicket.
He reached the break on 42, with Root sweeping confidently on his way to 28.