Perera took 4-34 off eight overs as Pakistan were skittled for a paltry 102 in Dambulla on Saturday.
Just three players reached double figures and Fawad Alam (38 not out) had little to no support as Pakistan made their ninth-lowest ODI total.
Dhammika Prasad (2-25 off six overs) and Lasith Malinga (1-17 off seven) got the ball rolling for Sri Lanka and they never looked back, needing less than 19 overs to chase down their victory target.
Tillakaratne Dilshan - who superbly ran out Pakistan captain Misbah-ul-Haq earlier - hit an unbeaten 50 from just 55 deliveries as Sri Lanka clinched the three-match series.
Pakistan won the toss and elected to bat but made a disastrous start as Prasad removed both openers Sharjeel Khan (zero) and Ahmed Shehzad (10).
Malinga then trapped Mohammad Hafeez lbw for one to leave Pakistan reeling at 14-3 before Misbah and Fawad appeared to steady the ship.
They added 33 runs in less than nine overs before Misbah was run out by Dilshan's pinpoint throw.
That proved the trigger for another collapse as Umar Akmal and Shahid Afridi fell playing big shots, dismissed for seven and two respectively.
Perera added the scalps of Sohaib Maqsood (seven) and Wahab Riaz (zero) before a 40-minute rain delay - taken at 81-8 - threatened to halt their momentum.
But while Pakistan edged over 100, their resistance did not last long, as Fawad, who hit three fours in his 73-ball knock, ran out of partners.
Sri Lanka's dominance was highlighted by star spinner Rangana Herath bowling just 2.1 overs, enough time for him to dismiss Mohammad Irfan, bowled for five, to end Pakistan's innings.
Sri Lanka made a fast start to their run chase, with Dilshan and Tharanga adding 46 in seven overs for the first wicket.
And although Mohammad Irfan (1-37 off seven) bowled Tharanga, and Kumar Sangakkara (two) departed cheaply, they were always in control.
Mahela Jayawardene added 26 before falling to Saeed Ajmal (1-10 off four) as Sri Lanka were just three runs from their target, but that allowed Dilshan to hit the winning runs with his ninth boundary.
The completion of the ODI series ends Pakistan's tour of Sri Lanka. They lost the two-match Test series 2-0.