Leg-spinner Rashid took five wickets to help bowl Ireland out for 126 before Hales struck 55 off 39 balls to lead England to their easy target.
It was the gentlest of starts to the summer for England, who are hosting the Champions Trophy in June before test series against South Africa and West Indies.
Ireland chose to bat after winning the toss and Ed Joyce and Paul Stirling shared an opening stand of 40. They advanced to 81 for two before a dramatic collapse where they lost their last eight wickets for 45 runs. Rashid completed figures of 5-27, his first five-wicket haul in one-day internationals.
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Jason Roy fell for a duck in the first over of the England reply but Hales smashed 10 fours and Joe Root made a fluent unbeaten 49 to guide his team home.
The second and final match of the series is at Lord's on Sunday.
(Reporting by Ed Osmond, editing by Mitch Phillips)
