The duo overcame occasional discomforts to deny India in the morning session with Mathews, who scored the last of his seven test centuries in 2015, on 90 not out, which included 11 boundaries and two sixes.
And when Indian bowlers Shami and Ravindra Jadeja ripped through Sri Lanka's top order it left the tourists facing another tough day to survive and save the series.
That Delhi is affected by severe air pollution is a well-documented fact and on the day of play, the levels were severe.
The net is closing in on Sri Lanka's hopes of saving the series with India after they finished day four 31-3 in pursuit of a mammoth target of 410.
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"Shami is fine. You will see him in action tomorrow", Dhawan told the media after the end of play.
In the earlier press meets, India had claimed that the Sri Lankans were using delaying tactics and not focussing on cricket.
"The bottom line is we got to play a Test match". But we as a group have a job on our hand.
India opener Shikhar Dhawan sympathises with Sri Lanka's players but feels conditions were not bad enough to stop play. "There are so many beaches in Sri Lanka and pollution level is less in places where there are beaches", he added.
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Beginning the day 405 runs behind India's first innings total of 536 for seven declared, the onus was on the right-handers to spearhead Sri Lanka's battle for survival at the Feroz Shah Kotla Stadium.
Brief Scores: India 536/7 December vs Sri Lanka 192/3 (Angelo Mathews 90 not out, Dinesh Chandimal 52 not out; Ravindra Jadeja 1/40).
The Press Trust of India said it was the first time in the 140-year history of Test cricket that an global side had taken to the field in face masks.
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