Lahiru Thirimanne led a stubborn Sri Lankan resistance campaign in the first Test on Saturday after England captain Joe Root's 228 had lifted the tourists' hopes of a quick victory.
Thirimanne made an unbeaten 76 and Kusal Perera 62 as Sri Lanka reached 156-2 in their second innings, needing another 130 to reach England's first innings 421.
Root's fourth Test double century was the highlight of the third day but England lost six wickets in the morning session which will not have made the captain happy.
Sri Lanka managed only 135 in their first innings but showed more steel as they came back to bat.
Perera and Thirimanne made 101 for the first wicket and after four straight Test zeros Kusal Mendis broke the spell and scored 15 patient runs before he gave a catch to England wicketkeeper Jos Buttler off Jack Leach.
Thirimanne gave one fiery catching chance to Dom Sibley diving in the gulley off Sam Curran's bowling. But he remained with Lasith Embuldeniya (0) at the end of the day making life difficult for the England attack.