Sadeera Samarwickrama (53 batting) and Priyamal Perera (40 batting) added 78 runs for the unbroken sixth wicket stand as Indian bowlers led by left-arm seamer Chama Milind (3/43) will hoping to clean up the lower half quickly on the final day in order to set up a series win.
Resuming on 11 for no loss, openers Hashan Dumindu and Minod Bhanuka added just 16 more runs to their stand before left-arm pacer Milind drew the first blood for the visitors.
Skipper Kusal Mendis made a fine 65 for the hosts striking 10 boundaries in 85-ball knock that included two sixes as well.
Sri Lanka lost two quick wickets of Mendis and Thilaksha Sumanasiri (4) as they slumped to 167 for five before Samarawickrama and Perera took charge.
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India's first innings hero spinner Kuldeep Yadav, who accounted for six scalps, didn't get any success today as the Lankan batsmen played him cautiously taking just 53 runs in his 30 overs.
Brief Scores:
Sri Lanka 1st Innings 212
India 393 for eight decl
Sri Lanka 2nd Innings 245 for five (Kusal Mendis 65, Sadeera Samarawickrama 53 not out; Chama Milind 3/43).