Misbah ul-Haq's side had been under immense pressure before the Pool B clash in Napier, having been hammered by India and West Indies in their first two games and then lurching to a 20-run victory over Zimbabwe.
While they were hardly explosive on a wicket that is considered the best batting surface in New Zealand, they did patiently build an innings of 339 for six.
Their bowlers then kept the shackles on UAE, though there was some doubt as to whether they had any real interest in pushing for an unlikely victory as they batted out their 50 overs to finish on a pedestrian 210-8.
Pakistan's towering opening bowler Mohammad Irfan was virtually unplayable for his first three overs in tandem with Sohail Khan, who took two wickets as UAE slumped to 25-3 in the 10th over.
Khurram Khan (43) and Shaiman Anwar (62) combined for an 83-run partnership but they were unable to score quickly enough as the overs ticked away and the game went through the motions.
Anwar has now scored 270 runs during the World Cup with two half centuries and a century.
The victory should reduce some pressure on Pakistan, who had been facing intense criticism from former players and pundits for the manner in which they had played during the tournament.
Shehzad, whose own poor run of form had been symptomatic of a top six that had not been scoring, looked desperately out of touch early in his innings.
He was also dropped twice but managed to somehow push, flick and caress his way to 93 as he and Haris Sohail put on 160 for the second wicket.
Shehzad was run out when his bat bounced up as he dived for the crease while completing a second run off Mohammad Naveed.
The 23-year-old trudged off having been in sight of the first century by a Pakistani at the 2015 World Cup.
Sohail scored 70 runs in the partnership with Shehzad before he fell during the batting power-play, which Pakistan had taken at the 30th over.
Sohaib Maqsood (45) and Misbah ul-Haq (65) then combined for a 75-run partnership as Pakistan increased the tempo with the captain falling in the 49th over, as Manjula Guruge (4-56) took two wickets in two balls.
(Editing by John O'Brien)
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