Sri Lanka, resuming their second innings at the overnight score of 167-2, moved to 292-3 by lunch on the third day, an overall lead of 199 with seven wickets in hand.
Left-handed Sangakkara followed his 92 in the first innings with an undefeated 87.
Jayawardene made amends for falling for one the first time with a stroke-filled 65, his 30th Test half-century that was studded with nine boundaries.
The Sri Lankan captain was dismissed just before lunch when he was caught down the leg-side by wicket-keeper Matt Prior, who was standing up to the stumps to fast bowler Matthew Hoggard.
New batsman Chamara Silva kept Sangakkara company at lunch on three.
Sangakkara and Jayawardene put on 122 for the third wicket after coming together at the fall of Michael Vandort's wicket at 166-2 the previous evening.
Sri Lanka's Australian coach Trevor Bayliss said on Monday that England will find it tough to chase more than 250 runs in the fourth innings on the slow wicket that is expected to crack up.
Sri Lanka were bowled out for 188 in their first innings and England replied with 281, with Muttiah Muralitharan grabbing six wickets on the way to surpassing retired Australian Shane Warne's world record tally of 708 on Monday.