The duo helped Sri Lanka score a formidable 563 for five at the close of play in reply to England's modest 265.
The hosts, starting the day on 264 for two, posted their second highest innings total against the tourists to establish a commanding 298-run lead.
Samaraweera and Jayawardene started cautiously, adding 70 runs during a turgid morning session, before upping the tempo during the afternoon and extending their six-hour partnership to 262 from 543 balls.
The third-wicket stand was the highest ever partnership at the Sinhalese Sports Club for any wicket and a record third-wicket stand against England, surpassing the 243 compiled by Sanath Jayasuriya and Aravinda de Silva at the Oval in 1998.
A weary England, who have dropped a total six catches during the Sri Lanka innings, including five during the Samaraweera-Jayawardene stand, eventually broke through in the afternoon.
Jayawardene, the more fluent of the pair, finished with 134 from 246 balls, having hit 14 fours and one six. It was his 10th Test hundred and his first for 18 months.
Samaraweera reached his third Test century soon after lunch -- the previous two were also scored at the Sinhalese Sports Club -- before being run out following a mix-up with Tillakaratne Dilshan.
Samaraweera scored 142 from 408 deliveries, having hit 13 boundaries in a painstaking innings that spanned just over eight hours.
Jayawardene pulled a short delivery from Andrew Flintoff to Paul Collingwood at deep square to end the partnership.
DROPPED CATCHES
England's players, kept awake into the early hours of the morning by a noisy party at their team hotel, were frustrated by a series of dropped catches and the rejection of several close lbw appeals.
Jayawardene was dropped in the gully on 71 and at long leg off a miscued pull on 74.
The first chance was extremely difficult as Mark Butcher flung himself to his left but Ashley Giles should have pouched a relatively straightforward chance running in from the boundary.
Jayawardene, on 96, was also fortunate to survive a leg-before shout off Gareth Batty off the last ball before lunch. Samaraweera should also have been caught at slip by Marcus Trescothick on 98.
After the loss of the third wicket pair and skipper Hashan Tillakaratne, who was bowled by Ashley Giles for 12, Dilshan (72 not out) and Upul Chandana (54 not out) shared an unbroken 107 partnership.
Flintoff was England's most penetrative bowler, taking two for 47 before leaving the field immediately after dismissing Jayawardene.
England's spin twins, Giles and Batty, toiled unsuccessfully on the slow-turning pitch, taking one for 296 from 101 overs between them.
The first two Tests were drawn after England's batsman defied Sri Lanka's spinners on tense final days.
Scoreboard
England (1st innings):
M.Trescothick c Jayawardene b Muralitharan 70
M.Vaughan c Jayawardene b Chandana 18
M.Butcher c Sangakkara b D.Fernando 23
N.Hussain lbw Vaas 8
G.Thorpe lbw Muralitharan 13
A.Flintoff c & b Muralitharan 77
G.Batty c Atapattu b Chanadana 14
C.Read not out 17
A.Giles run out 10
J.Kirtley lbw Vaas 1
J.Anderson lbw Vaas 1.
Extras: (4-b, 8-lb, 1-nb) 13
Total: (all out, 101 overs) 265
Fall of wickets: 1-78, 2-108, 3-114, 4-135, 5-139, 6-226, 7-236, 8-258, 9-259
Bowling: C.Vaas 17-5-64-3, D.Fernando 12-3-55-1 (1-nb), T.Samaraweera 4-1-11-0, U.Chandana 26-7-82-2, M.Muralitharan 40-21-40-3, S.Jayasuriya 2-1-1-0
Sri Lanka (1st innings):
K.Sangakkara c Trescothick b Kirtley 31
S.Jayasuriya c Trescothick b Flintoff 85
T.Samaraweera run out 142
M.Jayawardene c sub (Collingwood) b Flintoff 134
T.Dilshan not out 72
H.Tillakaratne b Giles 12
U.Chandana not out 54.
Extras: (6-b, 16-lb, 6-nb, 5-w) 33
Total: (for five wickets, 172 overs) 563
Fall of wickets: 1-71, 2-138, 3-400, 4-428, 5-456
Bowling: J.Kirtley 26-4-98-1 (3-nb), J.Anderson 24-5-85-0, A.Flintoff 18-0-47-2 (3-nb), A.Giles 60-16-159-1, G.Batty 41-4-137-0, M.Vaughan 1-0-5-0, M.Trescothick 2-0-10-0 (5-w).
Still to bat: M. Atapattu, C. Vaas, D. Fernando, M. Muralitharan
