Jayawardene batted for more than six hours for 119 in a Sri Lanka total of 381 for six when bad light stopped play for the third and final time.
The visitors, who were asked to follow on after scoring 192 in their first innings in reply to England's 551 for six declared, have an overall lead of 22.
Sajid Mahmood, who took three wickets in Sri Lanka's first innings on his Test debut, took another two in 13 balls on Sunday after the visitors had resumed on 183 for three.
