Ireland's second victory in as many matches have put them on top of their group, ahead of the Netherlands and Zimbabwe, who have won a match each out of two.
Ireland were 103 for three in 14.2 overs in pursuit of UAE's modest 123 for six when the heavens opened up. Under the D/L method, 83 was the par score for Ireland when it started raining.
Sterling was hit on his elbow when he tried to pull Sharif Asadullah in the first over of the innings. He hit two fours of the same bowler before the pain became unbearable, forcing him to retire.
Invited to bat, UAE openers started well putting on 35 runs in five overs, before Faizan Asif was run out. Shaiman Anwar top-scored for the Irish side with a 28-ball 30. Opener Amjad Ali made 20 while Amjad Javed scored a brisk 19 with the help of three fours towards the end.
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Ireland bowling was led by Paul Stirling (2/12) and Kevin O'Brien (2/17). The other bowlers chipped in with useful contributions as the UAE batsmen found the going tough in this crucial match.
There was a fourth-wicket partnership of 42 runs between Anwar and skipper Khurram Khan (16), but UAE kept losing wickets at regular intervals in the face of some inspired bowling by the Irish.
Placed third in the standings, Ireland have won the only match they have played so far, while UAE are yet to open their account.