Zaheer Khan took three more wickets to record his eighth five-wicket haul as India won the third and final test by an innings and 24 runs on the final day.
“I think the real tough task from now on is to maintain this performance,” said India captain Mahendra Singh Dhoni.
“The real tough job starts from here.”
Left-arm Zaheer dismissed overnight century-maker Kumar Sangakkara (137) caught behind in the day’s opening over to kill off any hopes Sri Lanka had of saving the test.
Resuming on 274-6 and needing 60 runs to make India bat a second time, Sangakkara edged the third ball to wicketkeeper Dhoni.
Zaheer then dismissed Rangana Herath (three) and overnight batsman Nuwan Kulasekara (19) in a fiery four-over spell to finish with five for 72.
“Zaheer is back in the rhythm and it was good to see the fast bowlers do well in India,” Dhoni said.
Off-spinner Harbhajan Singh then dismissed Muttiah Muralitharan for 14 as India wrapped up the tail in 7.4 overs.
“It was tough but India outperformed us in all three departments of the game in the last two tests,” Sri Lankan captain Sangakkara said.
“In this game, we nearly put 400 but (Virender) Sehwag came and took the game away from us.”
The 2-0 series victory saw India jump from third in the rankings to displace South Africa at the top.
“Fantastic to be at this position,” Indian batting great Sachin Tendulkar told the official broadcasters.
“I have been waiting a long time to get to this position. In fact just not me, (the) entire nation.”
Sri Lanka, who are still looking for their first test win on Indian soil, dropped from second place to fourth in the rankings, behind Australia.
Opener Sehwag, named player of the match and the series, scored a spectacular 293 and Dhoni cracked 100 not out to guide India to their highest innings total of 726 for nine declared.
Tillakaratne Dilshan scored a century and Angelo Mathews missed out on his maiden century by one run in Sri Lanka’s first-innings 393.
India opened up 1-0 lead by winning the second test by an innings and 144 runs after the first test ended in a draw.
Sri Lanka will play two Twenty20 internationals and five one-day internationals starting on Wednesday.
SCOREBOARD
Sri Lanka first innings: 393 (T. Paranavitana 53, T. Dilshan 109, A. Mathews 99, H. Singh 4-112)
India first innings: 726-9 dec (M. Vijay 87, V. Sehwag 293, R. Dravid 74, S. Tendulkar 53, V. Laxman 62, M. Dhoni 100 not out, R. Herath 3-240, M. Muralitharan 4-195)
Sri Lanka second innings (274-6 overnight)
T. Paranavitana lbw b Sreesanth 54
T. Dilshan lbw b Harbhajan 16
K. Sangakkara c Dhoni b Zaheer 137
M. Jayawardene c Dhoni b Zaheer 12
T. Samaraweera c Laxman b Zaheer 0
A. Mathews c Dhoni b Ojha 5
P. Jayawardene lbw b Ojha 32
N. Kulasekara c Laxman b Zaheer 19
R. Herath c Ojha b Zaheer 3
M. Muralitharan c Dhoni b Harbhajan 14
C. Welegedara not out 0
Extras (b-12, lb-1, w-1, nb-3) 17
Total (all out; 100.4 overs) 309
Fall of wickets: 1-29 2-119 3-135 4-137 5-144 6-208 7-278 8-282 9-307
Bowling: Harbhajan 34.4-5-80-2, Ojha 23-4-84-2, Zaheer 21-5-72-5 (nb-1), Sreesanth 13-4-36-1 (nb-2, w-1), Sehwag 9-2-24-0
