Sri Lanka, who won the preceding two-match Test series 2-0 against Pakistan, had fast bowler Nuwan Perera ruled out from the one-day series with a hamstring injury and inducted Lahiru Gamage.
Pakistan are taking on Sri Lanka in the first of the five ODI matches in Dubai on Friday.
Akila Dananjaya (50 not out) and Jeffrey Vandersay (25) delayed the result as they took Sri Lanka from 132-7 to 200-8 during their 68-run eighth-wicket stand but it was too little, too late.
Hasan's first victim was Kusal Mendis, caught behind for two, and when he cleaned up Milinda Siriwardana next ball the tourists were rocking at 67-5. Rumman Raees made a return to the starting line-up.
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Thirimanne hit three boundaries in his 74-ball stay.
But without the big shots and clever running between the wickets from the 35-year-old Malik, Pakistan would not have been in a position to take their total close to the 300-mark against a disciplined Lankan bowling attack. The veteran batsman struck his 40th fifty in ODI cricket as he scored 81 off just 61 balls with the help of five fours and two sixes.
Malik, declared man of the match, said he was happy to do the job. "Babar played well and Hafeez played a little cameo which set us well".
Dinesh Chandimal (4) was trapped leg before to give Raees his second and leave Sri Lanka reeling at 34 for 2. The 22-year-old Azam scored what was the sixth century of his fledgling ODI career and it was the flawless response to his critics after his failure with the bat in Pakistan's 2-0 Test defeat.
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But even Pakistan were in danger of losing their way in the middle overs of their own innings and it wasn't until Malik stepped onto the field that their fortunes changed.
He would add 64 with Fakhar (43) before the opener was beaten by Akila Dananjaya's googly a ball after hitting him out of the park.
The left-handed Zaman played well during his 45-ball 42 though, hitting four fours and a six.
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