The tourists were 212 for two at lunch on the third day after losing just one wicket in the morning session.
Sangakkara, yet to score a Test hundred at 'the home of cricket', was 73 not out and Jayawardene, whose three previous Lord's Tests had yielded two centuries, unbeaten on 29.
Their third-wicket stand was so far worth 61.
However, Sri Lanka were still 363 runs behind and requiring a further 164 to avoid the follow-on after Joe Root's maiden Test double century had taken England to 575 for nine declared.
Also Read
Kaushal Silva was then 62 not out and Sangakkara 32 not out.
Play resumed Saturday in gloomy overcast conditions that led to the floodlights being switched on.
But it was pace and bounce, rather than swing, that did for Silva.
The gutsy opener had added just one to his overnight score when, trying to sway out of the way of a James Anderson bouncer, he didn't lower his bat, with the ball grazing the face on its way through to wicketkeeper Matt Prior.
His exit brought in Jayawardene to partner Sangakkara in what was set to be the duo's last Test at Lord's.
Jayawardene showed his touch by deliberately uppercutting fast bowler Liam Plukett over the slips for four -- a shot made all the safer by England following the modern trend of doing without a third man.
Meanwhile, Sangakkara went to 50 off 102 balls, including six fours. Anderson, after a miserly opening spell of one wicket for 12 runs in seven overs, was replaced by all-rounder Chris Jordan.
Jayawardene lofted Ali's fifth ball Saturday for four and later swept the bowler, primarily a batsman, for another boundary.