James Anderson marked his comeback to England duty by taking two wickets, while Chris Tremlett struck on the ground where he made his name with southern county Hampshire.
Mahela Jayawardene was three not out and Thilan Samaraweera nought not out in the first Test ever played at the ground.
In the five overs possible between lunch and tea, England took two wickets for six runs.
Anderson's figures stood at two for 12 in nine overs, while Tremlett had an analysis of one for five in five.
Lancashire swing bowler Anderson, who missed the drawn second Test at Lord's with a side injury, was recalled in place of Steven Finn as England looked to build on a 1-0 series lead secured by an innings and 14-run victory in the first Test in Cardiff.
After England captain Andrew Strauss won the toss and fielded, Anderson struck in the 13th over.
Test debutant Lahiru Thirimanne, in for injured Sri Lanka skipper Tillakaratne Dilshan, who had his thumb broken by Tremlett while making 193 at Lord's, edged a drive through to Strauss at first slip and fell for 10.
Two balls later, the rain that had delayed the start by more than an hour returned and forced an early lunch with Sri Lanka 23 for one.
And five balls after an 81-minute rain break, 23 for one became 23 for two when Tharanga Paranavitana was lbw on the back foot to a full length swinging delivery from Tremlett.
Sangakkara, the third left-hander in Sri Lanka's top three, had to be persuaded to lead the side in Dilshan's absence after resigning the captaincy following the team's World Cup final defeat by India in Mumbai in April.
One of the world's leading batsmen, with an impressive Test average of more than 56 coming into this match, Sangakkara has often struggled in England.
And on Thursday he only made two before, trying to drive an Anderson delivery that cut away off the pitch, he was caught behind by Matt Prior.
It took Sangakkara's tally for the series to a meagre 65 runs at an average of 13.
