Zaman's 127 off 99 balls anchored the chase after an early wobble, while Salman Agha provided crucial support before Arafat Minhas' half-century paved the way for victory.
Pakistan chasing down a target of 326, finished on 331 with nine balls to spare to complete the joint-highest successful chase in an ODI final.
Earlier, Sri Lanka posted a formidable 325 for eight wickets, built around Kamindu Mendis' outstanding 131 off 128 balls and a fluent 77 from Pavan Rathnayake. The pair shared a crucial 146-run partnership before Pakistan struck late to curb any hopes of a 340-plus surge, with Shaheen Shah Afridi taking two wickets for 50 runs.
The victory secured Pakistan's first ODI tri-series title since 2008, when they beat India in the Kitply Cup final in Bangladesh, and made amends for their defeat to New Zealand in the final of a home tri-series in 2025.
Pakistan suffered early setbacks as Dilshan Madushanka struck twice in the powerplay, including the prized wicket of Babar Azam for a five-ball duck. Zaman and Saad Baig rebuilt the innings with an impressive 149-run partnership and Baig brought up his maiden ODI fifty before Maheesh Theekshana ended his knock for 74 off 75 balls.
Zaman accelerated after reaching his half-century and went on to register his 12th ODI century, partnering with Agha in a brisk 57-run stand that kept Pakistan firmly on course in the chase. The left-hander eventually fell to Madushanka, followed soon by Agha for 17, leaving Pakistan at 230-5. However, Minhas' and Hasan Nawaz's 94-run partnership ultimately carried the hosts to the target.
Sri Lanka made a strong start after being put in to bat, with opener Avishka Fernando and Kamindu Mendis adding 51 runs in the powerplay. Fernando's dismissal in the 18th over ended the opening stand, and Pakistan struck again soon after when captain Kusal Mendis fell to Agha, leaving the visitors at 109-2.
Kamindu and Rathnayake steadied the innings with a fluent 146-run partnership off 119 deliveries. The stand kept Sri Lanka firmly in control until Kamindu, who brought up his maiden ODI century, fell after hitting 12 fours and two sixes.
Pakistan fought back in the death overs, triggering a collapse as Afridi and Haris Rauf removed Dasun Shanaka and Rathnayake within the space of two overs. Sahan Arachchige provided a late cameo with a brisk 15 off 12 deliveries before falling to Naseem Shah.