Sri Lanka were leading by 212 runs with four wickets in hand at stumps, with Mathews sent back on the final ball for 141 and Sadeera Samarawickrama (21) still at the crease.
Chandimal (107) also notched up a century in a partnership that broke a record at the Sinhalese Sports Club that had stood for 32 years.
Arjuna Ranatunga and Asanka Gurusinha had put on 230 runs for the fourth wicket there in what is fondly remembered as the Shane Warne Test match, when the spin king helped Australia secure a thrilling 16-run win in 1992.
Mathews and Chandimal came together after three wickets had fallen in the morning session and Sri Lanka were still 50 runs behind.
The two senior batsmen saw off some accurate bowling by the Afghan fast bowlers on a wicket that had flattened out to the detriment of spinners.
Mathews was the first to the century, cutting Qais Ahmad past backward point for two runs. It was his 16th Test hundred.
His anticlimactic dismissal came when he smashed a full toss from Qais to the boundary but lost balance and crashed onto the stumps to be out hit wicket.
His innings topped his previous best in Sri Lanka of 122 against Pakistan in 2015. Chandimal got to his 15th Test hundred off Nijat Masood, clipping one past mid-on to the boundary.
Naveed Zadran was rewarded for his discipline when Chandimal was caught behind as Afghanistan found a breakthrough after 62 overs.
New captain Dhananjaya de Silva got off to the worst possible start on the next ball when he was run out.
He pushed one to mid-off and was trying to get off the mark, but Mathews was ball watching and Afghan skipper Hashmatullah Shahidi threw down the stumps at the striker’s end to find de Silva well short of the crease.
Afghanistan took three wickets before lunch on the second day after Sri Lanka resumed on 80 without loss. Nishan Madushka was the first to depart for 37 after hitting straight to Noor Ali Zadran at leg-slip off debutant Naveed Zadran.
Fellow opener Dimuth Karunaratne posted his 35th Test half-century in an aggressive knock that saw 12 boundaries off 72 balls. But the left-hander’s attempt to put away a full toss from Qais saw him caught at short mid-wicket by Ibrahim Zadran for 77.
Afghanistan were bowled out for 198 in the final session of Friday’s first day, after being put in to bat by the hosts.
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