Chasing India's 271 for 3, Sri Lanka reached their target with eight balls remaining after Jayasuriya and his fellow opener Romesh Kaluwitharana had launched a tremendous onslaught, blasting the first 50 from only 28 deliveries.
Manoj Prabhakar was hit out of the attack after conceding 33 in just two overs, but India looked to be regaining control after Jayasuriya was third out for a 76-ball 79.
However, Hashan Tillekeratne and his captain, Arjuna Ranatunga, shared a superb, unbroken fifth-wicket partnership of 131 to ensure victory. It left Sri Lanka, once regarded as the whipping boys of World Cup cricket, undefeated and sitting at the top of their group.
Tendulkar had earlier looked to have made the match safe for India as he powered his way to 137 at precisely a run a ball, his highest score in one-day internationals.
It was his second century of the tournament and he and his captain, Mohammad Azharuddin, who made 72 not out, put on 175 for the third wicket before Tendulkar was run out in the final over of the innings.
Tendulkar's display was laced with five sixes and eight fours, and it took him to 424 runs for only three dismissals in four matches in the tournament. In one over he punished the 20-year-old fast bowler Ravindra Pushpakumara, making his World Cup debut, for 23 runs.
Sri Lanka's opening assault was breathtaking, stunning the packed crowd at the Feroz Shah Kotla stadium. Kaluwitharana fell to a brilliant, diving catch by Anil Kumble in the covers after he had hit 26 off only 16 balls, but still the run rate hardly faltered, with 71 coming off the first seven overs.
Asanka Gurusinha helped keep up the pace before he was run out after making 25 in 27 deliveries. The tempo then slackened but Sri Lanka had still reached 137 by the 21st over when Jayasuriya's wonderful display came to an end as he lofted a high drive to Prabhakar down at long-off.
The dismissal of Aravinda de Silva two overs later put India right back in the match. Both wickets had fallen to the leg-spinner Kumble and he and Tendulkar, bowling off-spin, put a clamp on the scoring.
But Ranatunga and Tillekeratne calmly set about rebuilding the innings, picking up the run rate once Kumble and Tendulkar had finished their spells to guide Sri Lanka safely to victory. It had looked a difficult total to beat, but India had not reckoned with the brilliance of Jayasuriya.
(Sri Lanka won toss)
M Prabhakar c Gurusinha b Pushpakumara 7
S R Tendulkar run out 137
S V Manjrekar c Kaluwitharana b Dharmasena 32
*M Azharuddin not out 72
V G Kambli not out 1
Extras (b4, lb7, w11) 22
Total (for 3, 50 overs) 271
Fall: 1-27, 2-93, 3-268.
Did not bat: A D Jadeja, N R Mongia, A R Kumble, J Srinath, S A Ankola, Venkatesh Prasad.
Bowling: Vaas 9-3-37-0; Pushpakumara 8-0-53-1; Muralitharan 10-1-42-0; Dharmasena 9-0-53-1; Jayasuriya 10-0-52-0; Ranatunga 4-0-23-0.
S T Jayasuriya c Prabhakar b Kumble 79
K S Kaluwitharana c Kumble b Prasad 26
A P Gurusinha run out 25
P A de Silva st Mongia b Kumble 8
*A Ranatunga not out 46
H P Tillekeratne not out 70
Extras (b4, lb9, w3, nb2) 18
Total (for 4, 48.4 overs) 272
Fall: 1-53, 2-129, 3-137, 4-141.
Did not bat: R S Mahanama, H D B K Dharmasena, W P U C J Vaas, K R Pushpakumara, M Muralitharan.
Bowling: Prabhakar 4-0-47-0; Srinath 9.4-0-51-0; Venkatesh Prasad 10- 1-53-1; Ankola 5-0-28-0; Kumble 10-1-39-2; Tendulkar 10-0-41-0.
Sri Lanka beat India by six wickets.
Umpires: C J Mitchley and I D Robinson.