McDowell, who is defending the title he claimed last year, endured a rollercoaster round with three bogeys and four birdies in his first 10 holes.
After bogeys on the first and fourth, McDowell got back on track with a birdie from 20 feet on the fifth and another on the sixth, where his chip from the back of the green was travelling at pace before hitting the pin and dropping into the hole.
And when a superb approach to the seventh set up a tap-in to complete his hat-trick, the Portrush man was in red figures for the day and four under for the tournament.
Another birdie followed from five feet on the ninth, but a poor drive then cost the former US Open champion a bogey on the 10th.
McDowell dropped a further three shots on his remaining eight holes - including a double bogey at 14 - to eventually finish with a 2-over 73 that leaves him on 1-under heading into Sunday's final round.
Hoey also suffered something of a nightmare on the back nine after a steady start which saw him pick up two shots by the turn.
Another birdie followed at the tenth, but five dropped shots over the next five holes, including two double bogeys at 11 and 15, saw Ballymoney-born Hoey also finish with a 73 and remain tied with his compatriot McDowell.
American Kevin Sadler and local favourite Victor Riu are tied for the lead on 9-under heading into Sunday's final round.