The right-arm fast bowler finished with 5-30 while leg-spinner Devendra Bishoo took 3-46 to bundle Pakistan out for 208 in their second innings on a weary pitch.
At tea West Indies had wiped 23 off the target without losing a wicket and need another 130 for a consolation win after losing the first two Tests.
Opener Kraigg Brathwaite was 10 not out and with him Leon Johnson was batting on a chancy 12, having been dropped twice in successive overs from paceman Mohammad Amir.
Johnson again survived a slip catch on three when Sami Aslam dropped another straightforward opportunity at first slip off a luckless Amir, hurting Pakistan's chances of early wickets.
Earlier, Pakistan's chances of building a good lead ended when they slumped from 159-5 at lunch to lose their last five wickets for just 49 runs.
Opener Azhar Ali fell nine short of his 12th century when he edged Bishoo in the slip after initially deciding to sweep the ball but later changing his mind, only to hand a simple catch to slip.
Mohammad Nawaz helped Ali add another 41 for the sixth wicket but fell to Bishoo, who finished with 18 wickets in the series -- the most by a West Indian against Pakistan in a three-match series.
Holder then removed the tail, with wickets of Wahab Riaz (one) and Yasir Shah (nought) to improve on his previous best of 3-15 against England at Barbados in May last year.
Amir was foolishly run out after watching the long-on fielder Roston Chase save a six and throwing at the bowler's end with the batsman short of his crease.
Ahmed hit four boundaries during an enterprising innings before he chased a wide delivery from Bishoo and edged it to Darren Bravo at slip.
Pakistan lead the three-match series 2-0 after winning the first Test in Dubai by 56 runs and second by 133 runs in Abu Dhabi.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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