Sri Lanka were in deep trouble at 94-7 chasing a 238-run target but Jayawardene gave a scare or two to India, adding 81 for the eighth wicket with Thilan Thushara.
Jayawardene was the ninth man out after hitting one six and six fours in his 111-ball knock as Sri Lanka were bowled out for 204 under lights.
The home side now trail 2-1 in the five-match series.
The stiff resistance from the Sri Lankan skipper and Thushara came after fast bowlers Zaheer Khan (3-23) and Praveen Kumar (2-62) shared five wickets to raise India's hopes of an easy victory.
But despite their efforts, the asking rate kept climbing and Zaheer eventually broke the stubborn stand when he bowled Thushara, who was dropped twice.
Sri Lanka's bid to attack the new-ball bowlers from the beginning of their innings backfired, with Sanath Jayasuriya (13), Kumar Sangakkara (nine) and Chamara Kapugedera (12) all falling cheaply.
Jayasuriya smashed three fours off Kumar before he was dismissed in the bowler's third over.
Sangakkara was trapped leg-before by Zaheer immediately after cutting the bowler for a four, while Kapugedera was dismissed after lofting Kumar over midwicket for a six.
India threatened to reduce the match to a no-contest when Zaheer trapped Chamara Silva leg-before to leave the hosts reeling at 40-4 in the 10th over, but Jayawardene received valuable support from Thushara.
India earlier had impressive batting efforts from skipper Mahendra Singh Dhoni (76) and Suresh Raina (53) to thank for their 237 total after struggling at 91-4.
Dhoni put on 54 for the fifth wicket with Raina and 67 for the next with Rohit Sharma (32).
The Indian captain stepped up the run-rate with bold hitting in the closing 10 overs, which yielded 70 runs. He hit eight fours in his 23rd half-century.
Unorthodox spinner Ajantha Mendis finished with 3-56, including the wickets of Harbhajan Singh and Dhoni off successive balls in his last over. Seamers Nuwan Kulasekara and Thushara each took two wickets.
Scoreboard
INDIA:
V. Kohli run out 25
G. Gambhir lbw b Kulasekara 8
Yuvraj Singh c J’dene b Kulasekara 12
S.K. Raina run out 53
S. Badrinath c Vaas b Mendis 6
M.S. Dhoni c J’dene b Mendis 76
R.G. Sharma c K’gedera b Thushara 32
Harbhajan Singh c S’kkara b Mendis 2
P. Kumar not out 2
Zaheer Khan c Murali b Thushara 1
EXTRAS (B-2, LB-6, W-11, NB-1) 20
TOTAL (for nine wkts, 50 overs) 237
FALL OF WKTS: 1-39, 2-40, 3-62, 4-91, 5-145, 6-212, 7-229, 8-229, 9-237.
DID NOT BAT: M.M. Patel.
BOWLING: Vaas 10-2-33-0 (2w); Kulasekara 7-1-32-2 (2w); Thushara 9-1-36-2 (6w); Mendis 10-0-56-3 (1nb, 1w); Muralitharan 9-0-48-0; Jayasuriya 5-0-24-0.
SRI LANKA:
S.T. Jayasuriya c Dhoni b Kumar 13
K.C. Sangakkara lbw b Zaheer 9
C.K. Kapugedera lbw b Kumar 12
D.P.M. Jayawardene c Kumar b Patel 94
L.P.C. Silva lbw b Zaheer 1
T.M. Dilshan c Dhoni b Patel 16
W.P.U.J.C. Vaas b Harbhajan 0
K.M.D.N. Kulasekara lbw b Yuvraj 11
T. Thushara b Zaheer 30
B.A.W. Mendis not out 6
M. Muralitharan b Patel 6
EXTRAS (LB-2, W-4) 6
TOTAL (all out, 49 overs) 204
FALL OF WKTS: 1-18, 2-26, 3-37, 4-40, 5-58, 6-59, 7-94, 8-175, 9-192.
BOWLING: Kumar 10-0-62-2 (2w); Zaheer Khan 10-3-23-3 (1w), Patel 10-1-42-3; Harbhajan Singh 10-0-29-1; Yuvraj Singh 8-0-37-1 (1w); Sharma 1-0-9-0.
RESULT: India won by 33 runs.
UMPIRES: T.H. Wijewardene (Sri Lanka) and B.R. Doctrove (West Indies).
TV UMPIRE: M.G. Silva (Sri Lanka).
MATCH REFEREE: B.C. Broad (England).
MAN-OF-THE-MATCH: Mahendra Singh Dhoni.
NEXT MATCH Colombo (D/N), Tuesday.—AFP