Needing a draw to seal a series victory, the Sri Lankan batsmen appeared in no hurry to score runs on a slow turning pitch.
Resuming on their overnight score of 220 for five, Sri Lanka lost Prasanna Jayawardene (35) early when he hooked Mohammad Talha straight to Junaid Khan at deep fine leg.
Jayawardene added 73 runs with Mathews (91) for the sixth wicket.
Mathews, who scored 91 and 157 not out in the drawn first test in Abu Dhabi, continued to frustrate Pakistan and added 112 runs with Perera (95) before he holed out to Ahmed Shehzad at deep cover off Junaid.
The left-arm paceman trapped Rangana Herath leg before with his next ball for his third wicket to raise Pakistan's hopes of wrapping up the innings quickly.
But Perera continued to defy Pakistan, adding 72 for the ninth wicket with tailender Shaminda Eranga (25) and take the total past 400.
He fell in similar fashion to Jayawardene, his hook shot off Talha finding Junaid in the deep.
Pakistan managed to keep a lid on the scoring rate but were left to rue their bad luck during the day with a number of close appeals going against them.
(Writing by Sudipto Ganguly; editing by Justin Palmer)
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