Sri Lanka made late inroads as England slipped to 320 for six after Sam Robson had put them in control with his maiden Test hundred here on Satutday.
At close on the second day of the second Test, England, resuming at their overnight score of 36/0, had extended their lead to 63 runs.
Robson, who made his debut in the first-Test draw at Lord's last week, was the model of patience as he stroked a risk-free ton. Sri Lanka's three-man pace attack of Dhammika Prasad, Nuwan Pradeep and Shaminda Eranga rarely troubled Robson and Gary Ballance.
The two newcomers put on 142 for the second wicket although Ballance had an escape when he was given out lbw soon after lunch off the bowling of Rangana Herath.
Umpire Billy Bowden's decision, however, was overturned after a video review.
Ian Bell, playing in his 100th Test, looked set for a milestone century but was out after stroking his way to delightful 64.
Earlier, England lost captain Alastair Cook for 17 in the fourth over of the day when he edged Prasad to Kumar Sangakkara at first slip.