Coming together immediately after lunch when opener Kieran Powell became Mohammad Amir's third wicket with the innings in tatters at 71 for five, Chase batted with confidence and fluency for a top score of 63.
His sixth-wicket partnership with Dowrich was worth 118 runs, the wicketkeeper-batsman enhancing his reputation with a polished 56, the pair making a mockery of the West Indies' earlier struggles after they were put in to bat.
Yet it was Yasir Shah who removed both him and Dowrich off successive deliveries in the final session.
Made to look ordinary by the pair's positive play through the afternoon, the leg-spinner had the last laugh when he lured Chase into the lofted stroke and Wahab Riaz held an outstanding catch running back from mid-off almost to the boundary rope.
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At 189 for seven, Pakistan's hopes of dismissing the West Indies on the opening day were revived, only for captain Jason Holder (30 not out) and specialist spinner Devendra Bishoo (23 not out) to frustrate the visitors with an enterprising unbroken eighth-wicket stand of 55.
Earlier, Mohammad Abbas had a dream start to his Test career, having Kraigg Brathwaite caught at second slip by Younis Khan without scoring with his second delivery sharing the new ball with Amir.
It was an important early breakthrough as the opener had made history in their last Test match meeting with unbeaten scores of 142 and 60 that earned the Caribbean side a five- wicket win in Sharjah last November at the end of an otherwise miserable tour of the United Arab Emirates.
Maintaining a nagging accuracy, the left-arm fast bowler bowled both Hetmyer and Shai Hope, scattering the stumps with deliveries that jagged in sharply off a good length.
Pakistan's third seamer in their bowling armoury, Riaz, then removed Singh via a fine diving catch by Azhar Ali at backward square-leg to have the home side tottering at that point at 53 for four.
West Indies opted to omit Jermaine Blackwood from their final eleven to accommodate the debutants in the batting line-up, meaning there was no Jamaican in the home side for a Test match at Sabina Park for the first time since 1997 when, incidentally, the opponents were also Pakistan.
This is the 50th Test between the two nations and also the 50th Test match to be played at Sabina Park since the very first at the venue in 1930.
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