Pakistan now need 219 runs to win with more than two days to get that total.
The chase may yet be a difficult task on a surface which is offering much to spinners such as West Indies leg-break bowler Devendra Bishoo.
Bishoo has given himself a better chance with the ball thanks to a superb last-wicket partnership with Shivnarine Chanderpaul.
The Guyanese pair put on 48 for the final wicket -- the best partnership in the West Indies innings with last man Bishoo making 24 and Chanderpaul unbeaten on 36.
After resuming on 34-2, West Indies lost nightwatchman Kemar Roach, lbw to Ajmal, with the sixth ball of the day and wasted a review appeal by questioning the verdict.
The in-form Lendl Simmons then went for 21, caught by Azhar Ali at short leg of a rising delivery from Wahab Riaz.
The hope of the crowd was that Guyanese pair Ramnaresh Sarwan and Chanderpaul would provide some backbone to the innings but Sarwan gloved a sharply rising delivery from Ajmal to square leg.
Australian-born Brendan Nash then slipped and fell and was run out before Carlton Baugh inexplicably tried to slog Ajmal over midwicket but succeeded only in finding Umar Akmal.
After lunch captain Darren Sammy's disappointing form continued as he was trapped lbw by Abdur Rehman for nine.
The last wicket stand keeps West Indies hopes alive but despite the tricky track Pakistan will fancy their chances of taking a 1-0 lead in the two test series.
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