Sri Lanka, resuming the day on 14-1 after bowling India out for 249, added 100 runs in the 28-over morning session for the loss of only Michael Vandort (14).
Vaas reached the interval on 39 from 79 balls, having hit eight boundaries, and Sangakkara was unbeaten on 45 from 70 balls with five fours.
Zaheer Khan provided early hope for the Indians by trapping Vandort lbw with an inswinger.
He also came close to dismissing Sangakkara without scoring, when a thick edge flew just wide of the man at gully.
However, the patient Vaas and more aggressive Sangakkara were able to see off the early threat of the new ball and when batting became easier, a partnership started to blossom.
India, though, were left ruing a dropped chance at slip by Rahul Dravid when Sangakkara was on 36 just before lunch.
Middle order batsman VVS Laxman was unable to field after injuring his ankle prior to the start of play.
The three-match series is tied at 1-1.