After conceding a mammoth 333-run first innings lead, the visitors were struggling at 274 for six at close on the penultimate day which was marked by Sangakkara's resillient unbeaten 133 under immense pressure.
The Lankans are still trailing by 59 runs at the end of the day and will have to bat out of their skins to achieve the near-impossible task of saving the game on a last-day Brabourne track which was expected to assist the bowlers.
The Indians, on the other hand, will look to wrap up the remaining four wickets quickly tomorrow and clinch the three-match Test series with a 2-0 margin.
In Image: Kumar Sangakkara plays a lofted shot during his defiant century