Pakistan lost opener Shan Masood for two in the third over of the day after winning a crucial toss and decided to bat on a seemingly flat pitch at Sheikh Zayed Stadium.
At lunch Hafeez was unbeaten on 44 and Malik -- playing his first Test since 2010 -- was 36 not out, having added 77 for an unbroken second wicket stand.
England captain Alastair Cook used his bowlers in short spells to preserve their energies in the hot conditions, with paceman James Anderson the only wicket taker.
Anderson was then unlucky not to have Hafeez as Ian Bell dropped a regulation catch off the bat in the second slip. Hafeez was then batting on seven.
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When on 26, Hafeez cut leg-spinner Adil Rasheed for a boundary to complete his 3,000 runs in Test cricket in his 45th match. He has so far hit seven boundaries and Malik six.
Pakistan were forced to leave out leg-spinner Yasir Shah who was ruled out of the match with a back problem.
That forced Pakistan to include a third seamer in Imran Khan with left-armer Zulfiqar Babar as the only specialist spinner.
Malik was recalled to the Test side after Azhar Ali was ruled out on Sunday with a foot infection.
England handed a first Test cap to Rasheed, six years after his one-day debut in 2009.