The opener stroked 23 fours and hoisted two sixes in his 469-ball knock as he became the fourth Pakistani batsman to breach the 300-run mark before the hosts declared their first innings on 579 for three in the pink ball contest.
Azhar, 31, belted an overpitched delivery by Jermaine Blackwood through the covers for four to notch up his triple ton and an impressive record in the match -- becoming the first man to score a triple century in a day-night Test.
The right-hander, who enjoyed a fruitful 215-run partnership with fellow opener Sami Aslam (90) on Thursday, joined forces with Asad Shafiq (67) to pile on 137 runs for the second wicket. He added 165 with Test debutant Babar Azam (69).
Hanif Mohammad (337), Inzamam ul-Haq (329) and Younus Khan (313) were the previous triple centurions for Pakistan.
In only the second day-night Test, West Indies were 69-1 at the close of day two.