Opting to field after winning the toss, Holder (4/27) got useful support from fellow pacer Jerome Taylor, who returned figures of 3/36 to help the West Indies bundle out their opponents in 47.4 overs at the McLean Park.
Lower-order batsmen Nasir Aziz (60) and Amjad Javed (56) were the main contributors for the side batting first.
UAE would have been out for much less then what they eventually managed, had it not been for the seventh-wicket century partnership between Aziz and Javed.
Mixing caution with aggression, the two added 107 runs for the seventh wicket to not only steady the ship but also give their innings a semblance of respectability.
West Indies, who have two victories from five games, need to win this match to stay alive in the competition. Their prospects also hinges on the outcome of the day's next game between Pakistan and Ireland, and it is likely to boil down to net run rate to decide the third and fourth places from the group.
First up, though, the West Indies bowlers needed to bowl out the opposition to as low a total as possible, and they did just that.
Their dominance was evident from the fact that none of the UAE batsmen, barring Aziz and Javed, could get going after being invited to bat.
Mohammad Naveed (14) was the only other player to get to double digit, as the top-order batting put up a pathetic show in the face of some disciplined bowling form the West Indies pacers.
Andre Russell picked up 2/20, while there was one wicket for Marlon Sameuls, who bowled economically to concede 25 runs from his 10 overs.