Younis was unbeaten on 84 with skipper Misbah-ul-Haq 35 not out after Pakistan won the toss and opted to bat on a batting-friendly pitch at Sheikh Zayed Stadium.
Younis was lucky not to be dismissed in the last over before tea as part-timer spinner Kraigg Brathwaite dropped a straightforward catch off his own bowling when the batsman was on 83.
Younis, who missed the first Test as he recovered from dengue fever, has so far hit seven boundaries and one six after reaching his 31st half-century shortly after lunch.
Younis had added 87 for the third wicket with Shafiq (68) after Pakistan lost openers Azhar Ali (nought) and Sami Aslam (six) in the first hour.
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The normal red ball and daylight cricket returned in Abu Dhabi after the first Test was a day-night affair with the pink ball in Dubai, as Pakistan fought back from a poor start.
Pakistan, who lead the three-match series 1-0 after winning the first Test in Dubai by 56 runs, brought in Younis, Zulfiqar Babar and Rahat Ali as they made three changes to their line-up. Wahab Riaz, Mohammad Amir (both rested) and Babar Azam were the trio to make way.
West Indies were forced to leave out unfit wicket-keeper batsman Shane Dowrich, bringing in Shai Hope.
The third and final Test starts in Sharjah from October 30.
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