Agha hit 107 off 90 balls as Pakistan made 305 all out in 49.5 overs on Sunday after Sri Lanka captain Kusal Mendis won his fourth successive toss and chose to field.
Pakistan pace bowlers then overcame heavy dew and threatening half-centuries from Pavan Rathnayake (79) and Janith Liyanage (60) to dismiss Sri Lanka for 268 in 48.1 overs.
Agha was among seven Pakistan cricketers summoned back home at the end of August during a tumultuous tour of England after he had led the team in the first Test -- and this marked a triumphant return.
After being summoned home, Agha was later not only removed as Pakistan T20 captain but also lost his place in the T20 team that beat Sri Lanka 2-1 in the recent three-match series.
However, he scored prolifically in domestic cricket, including a triple century and forced his way back into the ODI side.
He revived Pakistan from 4-118 in the 22nd over with partnerships with Hasan Nawaz (37) and Arafat Minhas (18) before Sri Lanka hit back in the death overs.
Babar Azam had fallen for 45 off 57 balls but Agha snatched the momentum from Sri Lanka, completing his half-century off 48 balls before going on to raise his hundred with an edged boundary.
Eshan Malinga (4-46) and Asitha Fernando (3-59) denied Pakistan a big finish in the final five overs with multiple strikes as Pakistan, at 5-279, went on to lose their last five wickets for 26 runs.
Malinga bowled a double-wicket maiden over before No.11 Haris Rauf denied him a hat-trick.
When Sri Lanka batted, captain Shaheen Afridi picked up 3-55 while Naseem Shah pinned down Sri Lanka's top-order with impressive swing bowling to finish with 2-43.
Haris Rauf ran through the tail with 2-48 while seam all-rounder Faheem Ashraf grabbed 2-49, including the key wicket of Rathnayake.
Pakistan will play England in Rawalpindi on Tuesday in the second match of the tri-series.
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