For the UAE left-handed opener Amjad Ali topscored with a brilliant 79-ball 77 but once the Lahore-born batsman fell, wickets tumbled like nine pins with Mendis running through the middle and lower order with his beguiling action.
Amjad hit 13 boundaries and added 70 for the second wicket with Indika Batuwitarachchi who made just 14.
Mendis, playing in only his fifth one-day, had a previous best of 3-39 against the West Indies at Port of Spain earlier this year.
Sri Lanka, who also beat Bangladesh by 131 runs on Wednesday, topped Group A and qualified for the next stage of Super Four.
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Bangladesh, who beat the UAE by 96 runs on Tuesday also qualified for the next phase.
Earlier Sri Lanka rode on half-centuries from Mahela Udawatte and Mahela Jayawardene against a disciplined UAE bow