The wily spinner finished with 6-124 to secure his second 10-wicket haul in Test cricket
The wily spinner finished with 6-124 to secure his second 10-wicket haul in Test cricket after claiming four wickets in the first innings as West Indies were bowled out for 322 before tea on a weary fifth and final day pitch at Sheikh Zayed Stadium.
Shah had deprived West Indian batsman Jermaine Blackwood of his second Test hundred when he bowled him for 95 in the pre-lunch session.
West Indies, set a mammoth 456-run target for an unlikely victory, fought hard and batted for 108 overs with Shai Hope also scoring a fighting 41.
Hope and Devendra Bishoo put on 45 runs during their eighth-wicket stand before left-arm spinner Zulfiqar Babar (2-51) had Hope and Bishoo (26) caught to finish the match.
In between Babar's wickets, Shah had Miguel Cummins bowled for nought to finish the match with figures of 10-210, having taken 4-86 in the first innings.
Pakistan won the first Test by 56 runs in Dubai, leaving the third and final Test in Sharjah starting from Sunday inconsequential.
Captain Misbah-ul-Haq was delighted with the series win.
"It's a good win and I am very happy," said Misbah, who equalled Imran Khan's record of most matches as Pakistan captain with 48. But this is Misbah's 23rd victory while Imran only had 14.
"The pitch was not helping the spinners so it was tough to get West Indies out even on a fifth-day pitch but we have match-winners like Shah who bowled very well."
West Indies captain Jason Holder was pleased with his team's fighting spirit despite the defeat.
"We've shown signs of improvement," said Holder, who has now lost eight of his 11 Tests as captain.
"Unfortunately, we weren't able to start the game the way we like. They scored too many runs on the first day, we didn't bat well in the first innings. Pleased with the guys like Blackwood, the way they showed application."
Blackwood defied Pakistan's spin-cum-pace attack in the first session, adding 63 for the fifth wicket with Roston Chase (20) and another 57 with Hope for the sixth.
When it seemed Blackwood would complete his second Test hundred, Shah produced a beautiful delivery which kept straight and hit the batsman's pad, dislodging the stumps.
Blackwood hit 11 boundaries during his enterprising 127-ball stay.
Shah then trapped Jason Holder leg before for 16 to complete his five-wicket haul, the second in the series.
Resuming at 171-4, West Indian pair Blackwood and Chase batted without any problems for the first nine overs, but in the 10th of the day Shah produced a sharp turning ball which took the edge off Chase's bat to wicket-keeper Sarfraz Ahmed for an easy catch.
Pakistan took the second new ball with the score on 223-5 but Blackwood hit two boundaries in Sohail Khan's first over.
Shah then took two more wickets to derail the West Indies.