The English reached 324-9 and lead by 278 runs. Play was stopped 43 minutes early, at 4:34 p.m., at Pallekele International Stadium.
Play is scheduled to start 15 minutes early on Saturday.
England lost four wickets in the morning session, but captain Joe Root then hit his 15th test hundred.
With the England top order perishing for the sweep shot, both the conventional and the reverse, Root took a different route playing straight. The 27-year-old Yorkshireman hit some elegant drives and powerful cuts but fell for the reverse sweep, ruled leg before wicket to Akila Dananjaya.
Dananjaya then dismissed first innings top-scorer Sam Curran when he bowled him to pick up his third five-wicket haul in test cricket.
Adil Rashid drove the hat-trick ball to mid-off but lasted only 13 deliveries before being given out leg before wicket to Dananjaya. The batsman got a thick edge onto the pads but England didn't have reviews to contest umpire Sundaram Ravi's decision.
Dananjaya finished 6-106, his career best figures. His bowling has come under a cloud after being reported by match officials as suspect during the test in Galle. The bowler is likely to miss the next test because he has to go overseas for testing.
After the struggle before lunch, England recovered thanks to a 74-run stand between Root and Jos Buttler.
Root then added 82 runs for the seventh wicket with Ben Foakes, who was unbeaten on 51.
Root's chanceless knock came as a big relief for England as he had accumulated only 52 runs in three innings in the series. On all three previous occasions, he had been dismissed by a left-arm spinner, but this time he tackled Malinda Pushpakumara well. It is his second test hundred against Sri Lanka.
Suranga Lakmal, the lone seamer in the Sri Lankan attack, sent down only four overs in the innings as the hosts depended heavily on their four pronged spin attack.
Sri Lanka need to win to stay alive in the three-match series after England took a 1-0 lead in Galle with a comprehensive 211-run win.
England has not won a test series in Sri Lanka since 2001.