Alastair Cook scored a superb 243 led the hosts to a first-innings total of 514 for eight declared and Anderson dismissed Brathwaite as West Indies 44/1 before rain.
Tharanga will lead the islanders into the opening match of the ODI series in Dambulla on Sunday.
Starc out; Faulkner, Christian in for India tour in September and October, Tim Paine name for T20.
England were 348 for three at stumps on the first day of what is just the fifth day/night Test worldwide.
After an excellent 3-1 series win at home over South Africa, England all set to host its first day/night Test starts Thursday at Edgbaston.
Sri Lanka have announced their squad for the ODI series against India that begins on Sunday.
Umesh Yadav, Pandya, Dickwella also reach career-high rankings in latest update; Chinaman bowlers Kuldeep Yadav and Sandakan move up too.
India beat Sri Lanka by an innings and 171 runs in the third Test and claimed their first ever 3-0 series win overseas.
Yuvraj Singh axed, Rohit Sharma and Manish Pandey return to Indian team for Sri Lanka limited overs series.
India enforce follow-on after after Sri Lanka were bowled out for 135.