Malik made 63 off 49 balls while Akmal scored 50 off 46 balls. Their unbroken partnership of 114 runs steered Pakistan home with eight balls to spare.
UAE captain Amjad Javed took all three Pakistan wickets.
Earlier Shaiman Anwar scored 46 off 42 balls while Javed was unbeaten on 27 to help the UAE reach 130 runs after suffering a top order batting collapse.
Pakistan's pace bowlers Mohammad Amir, Mohammad Sami and Mohammad Irfan each claimed a wicket apiece to leave the UAE struggling at 12 for 3.
“We all know the first six overs have been crucial. If you survive, then you can play shots and that is what we did,” said Malik, who won the man of the match award.
India face Sri Lanka in a key clash on Tuesday. India are in dominant form in the tournament having beaten Pakistan and Bangladesh in their two matches so far.
The Asia Cup is seen as a warm-up tournament for the T20 World Cup that starts in India from 8 March.
UAE: Rohan Mustafa c Afridi b Sami 1, Muhammad Kaleem b Amir , Mohammad Shahzad c Sarfraz b Irfan 5, Shaiman Anwar c Sarfraz b Irfan 46, Usman Mushtaq c Nawaz b Afridi 9, Mohammad Usman b Amir 21, Amjad Javed not out 27, Mohammad Naveed not out 10
Total (six wickets; 20 overs): 129
Bowling: Amir 4-1-6-2, Sami 4-0-28-1 (w2), Irfan 4-0-30-2 (w1), Afridi 4-0-24-1 (w3), Nawaz 3-0-26-0 (w1), Malik 1-0-13-0
Pakistan: Mohammad Hafeez c Fahad b Amjad 11, Sharjeel Khan lbw b Amjad 4, Khurram Manzoor c Patil b Amjad 0, Umar Akmal not out 50, Shoaib Malik not out 63
Total (three wickets; 18.4 overs) 131
Bowling: Naveed 3.4-0-28-0, Amjad 4-0-36-3, Shahzad 4-0-19-0, Raza 3-0-20-0, Rohan 3-0-20-0, Fahad 1-0-8-0