Pairing up in the middle with the tourists on 106-5 chasing 276 for victory, the duo put on 147 before Pakistan reached their target off the penultimate ball to take a 1-0 lead in the three-match series.
Sri Lanka had recovered from an inauspicious start of their own earlier in the day at the Mahinda Rajapaksa International Cricket Stadium, eventually posting an imposing 275-7 after the match was reduced to 45 overs per side due to rain.
Having been restricted to 75-4, Sri Lanka were indebted to captain Angelo Mathews' 89 - his highest ODI score - as he combined to add 116 with Mahela Jayawardene (63).
After losing five wickets at the halfway stage of their reply, Pakistan looked in danger of falling to defeat, before the partnership between Maqsood (89 not out) and Alam (62) set up Shahid Afridi (14) to hit the winning runs off the bowling of Nuwan Kulasekara (0-56).
Having won the toss, Pakistan skipper Misbah-ul-Haq opted to field and saw early success as Tillakaratne Dilshan (six), Upul Tharanga (18) and the big wicket of Kumar Sangakkara (25) were all claimed inside the opening 15 overs.
Dinesh Chandimal's departure for six brought Mathews and Jayawardene together, and the experienced duo rebuilt the innings, before Ashan Priyanjan struck eight of his 15 balls to the boundary in making 39 not out at the end.
Ahmed Shehzad's 49 was the only score of note among Pakistan's top five, but Maqsood and Alam led the way, although the hosts will rue a missed stumping chance when the former was on 32.
It fell to Maqsood, who earned the man of the match award, and Afridi to finish the job.
While the game was progress, it was announced that the second ODI would now also be played in Hambantota, rather than in Colombo, due to a waterlogged outfield at the Premadasa Stadium.
The clash has also been brought forward a day, and will now be played on Tuesday rather than Wednesday.