Zaman's entertaining hundred and Arafat Minhas's robust 61 off 31 balls took Pakistan to a winning 7-331 in 48.3 overs in Saturday's clash as the Sri Lankan bowlers found it hard to control the wet ball because of dew.
Kamindu Mendis scored 131, his maiden ODI century, to earlier propel Sri Lanka to 8-325 while batting first for the first time in the tournament.
Zaman came into the final with only 31 runs in his last four innings and spent most of the time in the dressing room after he injured his right knee while fielding.
Pakistan lost Maaz Sadaqat for five and Babar Azam for a five-ball duck, much to the disappointment of the 31,265 home fans at Gaddafi Stadium, but Zaman revived the chase with 19-year-old Saad Baig, who made 74 off 75 balls. They put up a 149-run stand.
Sri Lanka's Maheesh Theekshana, playing his first match in the tri-series, missed out on claiming Zaman on 69 and 106, when he couldn't hold onto a return catch. Theekshana dropped Zaman again, a sitter on the boundary, after he reached his century off 84 balls.
Zaman's 99-ball knock finally ended in the 34th over when he was clean bowled by Dilshan Madushanka with Pakistan still 106 runs from victory. Madushanka took 3-63.
The wet ball couldn't help Sri Lanka as the young pair of Minhas and Hasan Nawaz (37 not out) kept their nerve before Asitha Fernando (2-72) added to the drama by bagging the wickets of Minhas and Faheem Ashraf off successive balls.
