Sri Lanka's former captain, who was stranded on an unbeaten 199 in the first Test at Galle, ensured the side avoided following-on before being out on 192 on the fifth and final day.
The hosts began the day needing 74 more runs to make Pakistan bat again and were dismissed for 391 in the post-lunch session in reply to Pakistan's 551-6 declared.
Pakistan, leading by 160 runs on the first innings, scored 100 for 2 in their second knock before skipper Misbah-ul Haq declared after tea.
Sri Lanka appeared disinterested in chasing the tough victory target of 261 in 37 overs and were 86-2 in 22 overs when the match was called off at the Sinhalese Sports Club.
Sri Lanka will head for the third and final Test in Pallekele from Sunday with a 1-0 lead, having won the opening encounter in Galle by 209 runs.
The home side, which began the day on 278 for 5, was steered out of trouble by an 89-run stand for the sixth wicket between Sangakkara and Angelo Mathews [ Images ] (47).
But Mathews's dismissal soon after lunch triggered a middle-order collapse in which Sri Lanka lost their last five wickets for 21 runs.
Young left-arm seamer Junaid Khan bagged his second five-wicket haul in Tests and spinner Abdur Rehman claimed four.