Imad Wasim top scored for his side with a 35-run knock. Anwar Ali and Rahat Ali picked up two wickets each to hand Quetta a comprehensive win. Watson was named Player of the Match.
Pakistan pacer Wahab Riaz and spinning all-rounder Haris Sohail are out due to injury.
With the two-Test series due to start on April 28, the Pakistan Cricket board said Rahat Ali had not yet recovered from a hamstring injury that he picked up during the first one-day international against Bangladesh earlier this month.
Rahat Ali was a surprise inclusion in Pakistan squad after injured pacer Junaid Khan was ruled out. The 26-year-old Ali has played just one one-day international, in 2012, and did not even feature in the 30-member probables list of the World Cup.
Rahat Ali played his only one-day international against Sri Lanka in June 2012, and was a surprise replacement for an injured Junaid Khan.
Rahat Ali has played just one one-day international, in 2012, and was not considered for any of the 10 one-dayers Pakistan played in the build-up to the World Cup
Live cricket score and ball-by-ball commentary from the fourth day of the first Test match between Pakistan and New Zealand at the Sheikh Zayed Stadium, Abu Dhabi on Wednesday.
Tom Latham's hundred went in vain as New Zealand were shot out for 262. Pakistan lead by 319 runs at stumps on Day 3.
Live cricket score and ball-by-ball commentary from the third day of the first Test match between Pakistan and New Zealand at the Sheikh Zayed Stadium, Abu Dhabi on Tuesday.