Ahmed Shehzad (three) was the only batsman out in the morning as Pakistan reached 57 for one at lunch after Mathews became the first captain in six tests to put the opposition in at the International Stadium.
But the plot changed quickly in the afternoon session as Pakistan slumped from 78 for one to 127 for six with the Sri Lanka pace trio picking up two wickets apiece.
Pakistan opener Khurram Manzoor (73) survived some nervous moments before completing his sixth half-century in tests and added 50 for the second wicket with Mohammad Hafeez (21).
Nuwan Pradeep was impressive on his recall to the test side after a year and finished with three wickets for 62 while Shaminda Eranga picked up the prized scalps of the experienced Younus Khan (13) and Misbah-ul-Haq (one).
Younus and Misbah departed in the space of an over in similar fashion, edging Eranga to wicketkeeper Prasanna Jayawardene.
Sri Lanka's other fast bowler, Suranga Lakmal, accounted for Manzoor and Asad Shafiq (six) while left-arm spinner Rangana Herath polished off the Pakistan tail to pick up three wickets, having given up a total of 26 runs in the innings.
Pakistan failed to capitalise on some dropped catches by the Sri Lankan fielders and lost their last eight wickets for just 58 runs.
(Writing by Sudipto Ganguly; editing by Ken Ferris)
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