At the break, Pakistan had their most experienced pair of Younus Khan (10) and Misbah-ul-Haq (nought) at the crease, still trailing Sri Lanka by 194 runs.
Pakistan lost Ahmed Shehzad in the penultimate over before tea after the opener made a well-compiled 58 with seven fours.
Shehzad's wicket was taken by off-spinner Perera as the batsman pushed forward and got an inside edge to wicket-keeper Niroshan Dickwella.
Shehzad had some nervous moments earlier when he successfully reviewed a lbw appeal off Herath on 37 and a run later survived a difficult leg side catch to Dickwella off Dhammika Prasad. Shehzad and Azhar Ali (32) looked like carrying Pakistan through to tea after putting together a partnership of 63.
But Herath broke through when the confident Azhar mistimed an ondrive and gave a straight forward catch to Angelo Mathews at short mid wicket. Earlier, Pakistan left-arm paceman Junaid Khan completed his fifth five-wicket haul against Sri Lanka but not before the hosts' tailenders frustrated them to add 59 valuable runs in the morning to be all out for 320 in their first innings.
Pakistan's hopes of finishing off the Sri Lankan innings quickly were stalled by Prasad (13), Herath (17) and Chanaka Welegedara (27 not out) who fought bravely against Junaid and Wahab Riaz.
Herath added 23 for the ninth wicket with Prasad before the latter was trapped leg before by Junaid for his fifth five-wicket haul in an innings - all against Sri Lanka.
Herath and Welegedara added a further 36 runs for the final wicket.
Welegedara, returning to test cricket after nearly two years, frustrated Pakistan by slamming five fours during a cameo knock that came off 30 balls.
It was finally left to left-arm spinner Abdur Rehman to finish off the innings when he found the edge of Herath's bat and the resulting catch was held by Younus Khan at slip.
Junaid finished with figures of five for 87 and Riaz had three for 88.
Sri Lanka lead the two-test series 1-0.