The pair had come together in chaotic fashion on the fourth evening in Galle, the tourists succumbing to a clatter of nerves as they slipped to 14 for three chasing just 74.
Resuming on 38 for three they went about their business with a renewed clarity, making light of any overnight concerns they or the England fans watching at home may still have harboured.
They finished with a stand of 62, turning an embattled start into a walk in the park and delivered the result that had seemed inevitable all the way back to the first afternoon when they hustled their hosts out for just 135.
The ball was still turning sharply but the scoring was brisk enough to erase any doubt, with the mission accomplished in 36 minutes and 9.2 overs.
Bairstow, who had been at least partly complicit in running out Root for one during the previous drama, led the way with 35 not out and had the honour of hitting the winning runs.
In doing so the Yorkshireman made it four overseas Test wins in a row – the previous three dating back to last winter's tour of South Africa – a streak last seen in the 1950s.
Having earlier cut his second ball of the day for four to third man, he wrapped things up with a second boundary as he stooped low and swept Dilruwan Perera round the corner to make it 1-0 in the two-match series.
Lawrence, meanwhile, completed a highly successful first appearance in England colours. With a dashing 73 already to his name from the first innings, he showed bundles of composure in entirely different circumstances and his willingness to take on a challenge such as this speaks well of the 23-year-old's readiness for international cricket.
He had one moment of fortune along the way when home skipper Dinesh Chandimal declining to review an lbw appeal from Perera that DRS would have upheld, but it was academic in the wider context.
Showing respect but not deference to the opposition and the tricky pitch, he was enterprising in his strokeplay and followed Bairstow's calm lead.
The latter is a veteran next to Lawrence, with this his 71st Test appearance, but he had last appeared in this format way back in 2019. After a composed 47, his knock here confirmed him as a viable long-term candidate for the number-three slot.