The 21-year-old right-hander notched a 139-ball 120 and added 82 for the second wicket with Sharjeel Khan (54) and 99 for the fourth wicket with Sarfraz Ahmed (35) after Pakistan were sent into bat on a flat pitch.
Pakistan were 260-6 after 44.3 overs when a floodlight failure stopped play for 70 minutes, before the match was reduced to 49-overs-a-side.
Under the Duckworth-Lewis method, West Indies need 287 to win in 49 overs.
Azam's two strong partnerships laid the foundation of the total after Pakistan lost skipper Azhar Ali off the first ball of the match, caught behind off paceman Shannon Gabriel.
Sharjeel hit six boundaries and three sixes in an aggressive 43-ball knock before miscuing a drive off spinner Sulieman Benn and was caught at short third man.
Shoaib Malik fell to spinner Sunil Narine for six and from 93-2 both Azam and Ahmed batted sensibly, rotating the strike and hitting boundaries off bad balls.
Azam, whose previous best of 83 came against New Zealand at Auckland earlier this year, reached his hundred with a single off Narine.
Imad Wasim (24) and Mohammad Nawaz (19) gave final touches after the resumption as Pakistan added 24 more runs after the delay.
Paceman Carlos Brathwaite was the pick of the West Indies bowlers with 3-54.
The second match will also be played in Sharjah, on Sunday, while the third will be in Abu Dhabi on Wednesday.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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