Utilizing opener Virender Sehwag as a runner due to cramp, the elegant middle-order batsman scored his 17th Test hundred to remain unbeaten on 103, scored off 149 balls with 12 fours.
Suresh Raina, who helped in an unbroken sixth-wicket stand of 87, finished the match off in style shortly before the scheduled tea break by clouting Chanaka Welegedara for six to remain 41 not out as India chased down the 257 needed for victory.
Laxman was also involved in an important fifth-wicket partnership of 109 with Sachin Tendulkar, who scored 54 before being dismissed by Suraj Randiv as the off-spinner captured his first five-wicket haul in Test cricket.
In the final day morning session, Sri Lanka missed a golden opportunity to remove Tendulkar cheaply when he was put down by Tillakaratne Dilshan at forward short-leg with his score on 18.
The prolific batsman and cricket's most-capped test player made Sri Lanka pay for that early lapse by recording his 56th test half-century that included three boundaries.
Sri Lanka's only success of the morning was the wicket of nightwatchman Ishant Sharma, who was caught at short mid-wicket for four off Randiv after India had resumed on 53-3.
