The visitors, chasing a tough victory target of 510, were bowled out for 300 in their second innings just before stumps on the fourth day.
Pakistan finally found their backbone in second inning as Asad Shafiq and Younis Khan defied Sri Lanka for nearly two sessions on the fourth day in Galle.
Both provided a 151-run stand for the fifth wicket, before both fell on either side of the tea interval.
Off-spinner Suraj Randiv, who claimed four wickets in the first innings, took three more in the second to fashion Sri Lanka’s emphatic win.
Sri Lanka 472 & 137/5d
Pakistan 100 & 300 (114.0 overs)