At the close of the second day the pair, who came together with the total on 14 for two in reply to South Africa's 169 on Thursday, had taken the total to 485 for two.
Captain Jaywardene was on 224 and Sangakkara had scored 229 in an unbroken third-wicket partnership of 471.
The stand was the highest for any wicket against South Africa, surpassing the 385 scored by Steve Waugh and Greg Blewett at Johannesburg in 1997, as well the second highest partnership in the history of Test cricket.
The only larger partnership is the 576 scored by team mates Sanath Jayasuriya and Roshan Mahanama against India at Premadasa International Stadium back in 1997, the match where Jayawardene made his debut.
The hosts, who resumed on 128-2, have now stretched their lead to 316 runs and, with eight wickets still intact and three days still to play, have established a virtually impregnable position from which to force a victory.
Sangakkara, dropped in the gully and bowled off a no ball before reaching double figures, was the more aggressive of the pair during the morning session and reached his 10th Test hundred just before lunch and his fourth double hundred during the final session.
ELEGANT JAYAWARDENE
The 28-year-old left-hander, relieved of his wicket-keeping responsibilities for this match, had stroked 31 stylish boundaries from 307 balls at the Sinhalese Sports Club Ground.
Jayawardene, Sri Lanka's captain in the absence of the injured Marvan Atapattu, provided rock-solid support with a flawless and elegant 15th Test hundred that was then converted into his third double hundred with a six over mid-wicket.
The 29-year-old right-hander finished the day struck 27 fours and one six from 356 deliveries.
"We did know anything about the records and just tried to bat session by session to keep South Africa down," Jayawardene said.
"We've always enjoyed batting together because we are both positive players and complement each other in many ways."
The closest the tourists came to making a breakthrough was off the final over of the day when a thin edge off left-arm spinner Nicky Boje just evaded the gloves of wicketkeeper Mark Boucher.
South Africa's lacklustre bowlers, unable to find their best rhythm after a 10-week break, toiled throughout on a pitch that was slow and flat.
Dale Steyn was statistically the most successful bowler after his new ball strike on Thursday, finishing with figures of two for 98 from 19 overs.
However, Boje was the most effective, clamping down on Sri Lanka's run rate as he bowled over the wicket into the rough, occasionally extracting sharp turn and bounce from the bowler's foot holes.
Scorecard:
South Africa 1st innings: 169 (A. de Villiers 65; M. Muralitharan 4-41, D. Fernando 4-48)
Sri Lanka 1st innings (Overnight: 128-2)
U. Tharanga c Boucher b Steyn 7
S. Jayasuriya lbw b Steyn 4
K. Sangakkara not out 229
M. Jayawardene not out 224
Extras (b-8 lb-4 nb-7 w-2) 21
Total (for 2 wickets, 112 overs) 485
Fall of wickets: 1-6 2-14
To bat: T. Dilshan, C. Kapugedera, P. Jayawardene, F. Maharoof, L. Malinga, D. Fernando, M. Muralitharan
Bowling
M. Ntini 18 - 3 - 56 - 0 (nb-1)
D. Steyn 19 - 1 - 98 - 2 (nb-6 w-1)
A. Nel 16 - 0 - 80 - 0
A. Hall 17 - 1 - 69 - 0
N. Boje 35 - 3 - 131 - 0
J. Rudolph 5 - 0 - 32 - 0
A. Prince 2 - 0 - 7 - 0 (w-1)
