Ireland needed just four deliveries to wrap up an innings-and-26-run victory in the first match of their ICup campaign.
William Porterfield's men took the maximum 20 points available after ending the UAE's last wicket stand in the first over of the morning to complete a comprehensive victory in Malahide.
The UAE managed to take the match to the final day but last pair Manjula Guruge and Mohammad Naveed could not force their hosts to bat again.
They closed on 251 for nine on Thursday and Naveed added just two runs to the score before he was out next ball, finding only the hands of Dockrell after attempting to loft Craig Young over the infield.
It was fitting that the Irish pair combined to end the match, having each taken seven wickets in the match.
Ireland join Namibia at the top of the table and will play the African side in the next round of the competition later in the year.