Azmoun broke the deadlock with a clinical finish in the 58th minute, and then capitalized on a one-on-one situation with Ajman keeper Ali Al Hosani to double the scoreline five minutes later.
The brace took Iran international’s tally to three goals in as many appearances – first in the starting XI – for Shabab Al Ahli following a three-year move, worth from €5 million, from German Bundesliga champion Leverkusen.
Elsewhere in the UAE League Cup first round, ex-Sepahan striker Shahriar Moghanlou found the net from the spot in the 85th minute, with Mahdi Qayedi providing Brazilian Caio Eduardo with an assist, but Ittihad Al Kalba suffered a 3-2 defeat against AFC Champions League champion Al Ain at home.