At the break, Sri Lanka needed only 67 runs to avoid follow-on, which will be a big step towards taking the match into the fifth day with an aim for a draw.
Under fire for his below-par show in the preceding games, Mathews dug deep into his reservoir of experience to score his eighth Test hundred and added 181 runs in 79.2 overs with the in-form skipper Chandimal.
Mathews hit 14 boundaries and two sixes before Ravichandran Ashwin got one to drift away and as the former captain shaped up to play for an off-break, the resultant tickle was accepted by Wriddhiman Saha.
It was a day where the home team bowlers were left frustrated due to a benign pitch and butter fingers of their fielders.
Mathews was dropped thrice -- on 6, 98 and 104 by Virat Kohli, Rohit Sharma (both slips) and substitute fielder Vijay Shankar at mid-off. Chandimal was also dropped once during his innings.
Ravindra Jadeja (1/63 in 36 overs) bowled his customary tight lines but with not much help off the pitch, he was easily negated by the batsmen.
Ashwin (1/50 in 21 overs) was strangely underbowled considering that the two new ball bowlers have between them sent down 45 out of 102 overs.
Such had been their Indian dominance that Mathews and Chandimal put up the first century stand of the series. It also helped that two of Sri Lanka's most experienced batsmen shouldered the responsibility under pressure.
Normally known for his flamboyance, Chandimal, who has often been referred as 'Rohit Sharma of Sri Lanka' for his immense talent, curbed his natural instincts and showed discretion in his shot selection.
The Indian bowlers could not be faulted despite little assistance from the track.
Ishant Sharma (1/80 in 23 overs) got some of the deliveries to rear up awkwardly, but the Lankan duo did not do anything impetuous, leaving most of them alone.
Ishant, in particular, bowled a testing spell to Mathews, with some of the deliveries coming into him after hitting the seam.
After the first hour, Kohli brought back Mohammed Shami (1/65 in 22 overs) to make good use of the old ball, but there was not much reverse swing on offer.
In the morning, Chandimal hit a gorgeous cover drive and Shami responded with a well-disguised bouncer. He followed that up with one into his body that Chandimal tried to tuck away. The ball was in the air but fell agonisingly short of Ajinkya Rahane at leg gully. The skipper was on 43 then.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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