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Sri Lanka fast bowler Suranga Lakmal threw up twice in the morning session amid choking smog at New Delhi's Feroz Shah Kotla stadium, followed by Indian pacer Mohammed Shami later in the day.
Dhananjaya de Silva was batting on 13 and Angelo Mathews was yet to open his account when bad light stopped play on the fourth day of the Test.
Spinner Ravindra Jadeja struck twice in an over in the final session to rattle Sri Lanka's daunting chase.
The hosts, who lead the three-match series 1-0, need another seven wickets to claim victory.
The match has been marred by severe pollution, with Lakmal returning to the dressing room briefly and Shami vomiting in the middle of his wicket-taking over in the closing session.