Kumar Sangakkara's first Test hundred at Lord's helped the tourists but England remained in control of their series opener with Sri Lanka on Saturday.
The tourists were 7-415 at stumps on the third day, with left-hander Sangakkara's 147 key to their avoiding the follow-on.
The 36-year-old also became the first man to score hundreds in three consecutive innings on three separate occasions in Test cricket.
Sangakkara's 182-ball century was his 36th in 123 Tests.
England, however, still lead by 160 runs after Joe Root's maiden Test double century had taken them to a total of 9-575 declared.
Sangakkara was involved in partnerships of 97, 126 and 96 with Kaushal Silva (62), Mahela Jayawardene (55) and Sri Lanka captain Angelo Mathews (79 not out) respectively.
He was all assurance until caught behind off Moeen Ali to give the debutant off-spinner his first Test wicket.
"A hundred at Lord's is something I always wanted," the 36-year-old Sangakkara told Sky Sports.
"It feels very special to get on the honours board," added the left-hander, the seventh Sri Lankan to score a Test hundred at Lord's.
England captain Alastair Cook, often accused of lacking imagination, tried to unsettle the batsmen with unusual field placings and angles of attack.
But his bowlers were largely frustrated by Sangakkara, whose career batting average of 58.53 has only been bettered by players who've appeared in at least 25 Tests by Australia's Don Bradman (99.94) and the England duo of Herbert Sutcliffe (60.73) and Ken Barrington (58.67).
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