An unbeaten century from skipper Angelo Mathews backed up by a steady knock from Kusal Perera (70) helped Sri Lanka post 249/6 at tea on the fifth day of the third Test at the Sinhalese Sports Club (SSC) Ground here on Tuesday.
However, India pulled things back at the end of the session as off-spinner Ravichandran Ashwin got rid of Perera, breaking a 135-run partnership.
Mathews and Rangana Herath remained unconquered on 110 and 3 respectively in their chase of 386.
India still require four wickets to win whereas the hosts need 137 runs to clinch the contest.