Skipper Misbah-ul-Haq, 10 not out at the break, will look for quick runs to put pressure on the West Indian batsmen as they seek to take a 1-0 lead in the three-match series.
Ali has stolen the spotlight in just the second ever day-night Test, played with a pink ball, surpassing his previous best of 226 against Bangladesh in Dhaka last year.
The 31-year-old right-hander dominated the bowling and has encountered few problems in sighting the refined pink ball with a modified black seam, having so far hit 22 boundaries and two sixes during his 436-ball innings.
He added 215 for the first wicket with opener Sami Aslam (90) on the first day and then had two further big partnerships, putting on 147 with Asad Shafiq (67) and another 165 for the third wicket with debutant Babar Azam, who made 69.
Azam, given his first Test chance after scoring three hundreds in as many one-day matches in Pakistan's 3-0 rout of the West Indies, batted with authority.
He finally fell to leg-spinner Devendra Bishoo, whose figures of 2-105 lead a struggling West Indian attack.
Earlier Ali was given another lifeline when Jermaine Blackwood dropped a regulation catch off spinner Roston Chase in the slips with the Pakistani opener on 190.
Resuming at 279-1, Pakistan lost one wicket in the first session when Shafiq gave a return catch to Bishoo.
Ali continued from where he left off after resuming on 146, reaching his 150 with a single and then hitting a six and a boundary off Chase to send Pakistan past 350.
Shafiq then reached his 15th Test half-century with a well-timed four off Bishoo before missing out on a big score when he mistimed a straight drive.
Australia and New Zealand played the first day-night Test in Adelaide last year, the first-ever such fixture in Test cricket's 140-year history.
This three-match series will continue in Abu Dhabi (October 21-25) and Sharjah (October 30-November 3).
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