Needing 164 to win, the English faltered when reduced to 89 for four, but opener Dominic Sibley and Jos Buttler shared an unbeaten 75-run partnership to lead team to the victory
The first two Tests will be held in Chennai, beginning on February 5, while the next two will be played at the renovated stadium at Motera in Ahmedabad
England ensured it didn't have any more hiccups in erasing the remaining 36 required on the last day after Sri Lanka had set up a tricky 74-run target on a turning wicket.
Joe Root's team, missing Ben Stokes and Jofra Archer, need a convincing win in the two-match series to keep alive their hopes of reaching the World Test Championship final
Ravindra Jadeja is out of first two Tests against England. He will need 4-6 weeks minimum to recuperate and complete rehab which rules him out of first 2 tests, said BCCI source
The measures, which include a stay-at-home order and the closure of schools to most pupils, were announced by UK Prime Minister Boris Johnson on Monday.
Joe Root's team will immediately go into a secure bubble on their arrival which comes two days after authorities deployed top military officers to help contain coronavirus cases
Besides England, lockdowns were also introduced in Scotland and Northern Ireland, while restrictions that were eased for Christmas Day in Wales were re-imposed on Saturday
It is understood that young Shubman Gill, after a couple of impressive knocks in the warm-up games, is seen as a replacement of Shaw as senior star Rohit Sharma will not be available until the third Test match in Sydney.