Mahela Jayawardene scored a superb unbeaten 167 and Michael Vandort made 138 as Sri Lanka reached 379 for four at close of play on the third day of the second Test on Tuesday.
Sri Lanka, who resumed the day on 105 for two, overhauled England's first innings total of 351 all out for a 28-run lead with six wickets remaining.
Jayawardene's innings, his 20th Test hundred, spanned 367 deliveries and included 13 boundaries and one straight six.
The innings carried the 30-year-old past 7,000 Test runs to make him the highest run scorer in Sri Lanka's Test history.
The record was previously held by the now retired Sanath Jayasuriya, who finished with a career tally of 6,973 runs.
Skipper Jayawardene came to the wicket on Monday evening with Sri Lanka in trouble on 22 for two but lifted the hosts into a strong position with a 227-run third-wicket partnership with Vandort.
Vandort's hundred was the fourth of his career and spanned 259 deliveries, including 18 fours and one swept six.
England broke through with the second new ball when left-armer Ryan Sidebottom, trapped Vandort lbw midway through the afternoon but Jayawardene then added 128 runs with Chamara Silva (49).
Steve Harmison finally claimed another breakthrough just before the close with a short delivery that rose steeply on Silva and was fended off to gully.
In the morning, the closest England came to breaking through were a couple of streaky edges through the slips by Vandort off the quick bowlers.
Slow left-armer Monty Panesar, who finished with 0-111 from 32 overs, spun the ball sharply at times, especially when bowling over the wicket into the rough.
But on an increasingly placid pitch Sri Lanka's batsmen were rarely troubled by the England attack
Sri Lanka won the first Test in the three-match series by 88 runs.
