Needing 197 runs to achieve a historic series win, Sri Lanka were 60 for two at the close of play on Day 2.
At stumps, Sri Lanka were 88 for four in reply with Angelo Mathews not out 27 and Roshen Silva on 15.
Tamim Iqbal suffered an injury on the wrist in the second over of Bangladesh's innings against Sri Lanka when he was hit by a short ball from Suranga Lakmal.
Shane Dowrich's second Test century put the West Indies in control of the first Test against Sri Lanka as the home side declared their first innings at 414 for eight.
Suranga Lakmal led Sri Lankan bowlers on a confidence-boosting rampage to skittle out Bangladesh for 82 on Thursday and guide his side into the final of the Dhaka tri-nation tournament.
Veteran seamer Lasith Malinga has been ignored for the upcoming T20I series against India.
Stand-in captain Rohit Sharma scored his 3rd ODI double-century against Sri Lanka at Mohali.
Sri Lanka batting coach Thilan Samaraweera said the bowlers let the team down in a match where they conceded 50-60 runs too many.
Suranga Lakmal registered career-best ODI figures of four for 13 to help Sri Lanka dismiss India for a paltry 112
Suranga Lakmal ended with figures of 4/13 in 10 overs in registering Sri Lanka's first ODI win 13 matches as they beat India by seven wickets.
Mahendra Singh Dhoni scored a brilliant half-century to help India cross the three-digit mark.
Delhi's viability as an international sports venue has been called into question after Sri Lankan players complained of breathing problems due to smog and continued to wear anti-pollution masks.
The visiting Lankans were set an improbable victory target of 410 to level the three-match series.
The Sri Lankan Test captain Dinesh Chandimal was left out of the 15-man squad announced on Tuesday.
Five overs into India's 2nd innings, Sri Lankan players, Suranga Lakmal in particular, were once again seen in strife.
Shikhar Dhawan, who made a brilliant 94 in the Nagpur Test, scored 23 off 35 deliveries before being dismissed by Dilruwan Perera.
India vs Sri Lanka, 1st Test, Day 3 Highlights: Sri Lanka reached 165 for four at stumps after bundling out India for 172 on the third day of the opening Test at the Eden Gardens on Saturday.
Cheteshwar Pujara was the lone Indian batsmen to produce some fight against the Sri Lankan bowling attack on a green top in overcast conditions.