Hoey briefly held a three shot lead with another birdie at the first, but he was unable to shake off a revitalised McDowell, who was reaping the rewards after linking up again with his former coach Clive Tucker.
After dropping a shot at the sixth, McDowell birdied the ninth and 10th to close within two of Hoey once more, while McIlroy had increased the Northern Irish presence on the leaderboard yet further.
McIlroy, who opened with a 63 in The Open Championship at St Andrews last year before crashing to a second round of 80, was six under for 15 holes and into a share of third on 13 under, alongside England's Simon Dyson who was nine under for his round with three to play.
Dyson was unable to pick up any further shots, leaving a birdie putt on the 18th inches short and having to settle for a round of 63, equalling the course record for the extended layout set by McIlroy in the Open last year.
"I'm very, very happy with the day," said Dyson, who is 30th in the Official World Golf Ranking after two wins this year. "I didn't realise it was for the course record otherwise I might have hit it a bit harder.
"But it's a good name to share it with."
At 13 under par, Dyson shared fifth place with McIlroy - who also parred the last four holes for his 66 - but Hoey was now 19 under after holing a bunker shot for a birdie on the third at Carnoustie.