Akhtar bagged the scalps of Upul Tharanga (11), Chamara Kapugedara (2) and Farveez Maharoof (1).
Sri Lanka were well served by Jayawardene and captain Sangakkara who raised 83 fighting runs for the third wicket.
The hosts were in a spot of bother at 36 for two when the two most experienced batsmen in the side came up with the rescue act.
At 150 for five in the 32nd over, Lanka were still in the woods. But Mathews found responsive and gutsy allies in Kulasekara, with whom he raised 43 runs for the eighth wicket, and Malinga (12) to take his side to a winning total, a score that Pakistan eventually failed to chase.
Image:Mahela Jayawardene was in fine nick for Sri Lanka, making a half century