Logan's first-half header and a gift to Hayes on the hour were enough to see off the visitors, who started brightly but were quickly nullified
The Dons were reduced to 10 men as substitute Jayden Stockley saw red, but it was too late to affect the outcome
The visitors were first to threaten, despite a magnificent tackle from Logan on striker Isma Goncalves in the centre of the penalty area
The ball broke to Arnaud Djoum who squared for Sam Nicholson, but the winger somehow sent his shot well over the bar
Logan was in the right place at the right time again midway through the first half, ghosting between Lennard Sowah and Nicholson to meet Niall McGinn's cross from the left and head home the opener.
There was an immediate tactical shift by Dons boss Derek McInnes, moving his defensive line high up the field to nullify the threat of target man Isma, and it effectively took the Hearts front four out of the game.
While the game was certainly not boring, the tactical battle that was ensuing kept chances at a premium in the first half.
However Aberdeen had the ball in the net again early in the second half
Graeme Shinnie's touch to pluck the ball out of the air was sublime, and though his 25-yard strike was saved, Adam Rooney was on hand to turn the ball home.
Rooney's joy was short-lived, though, as he had strayed into an offside position and the goal was rightly chalked off.
Kenny McLean came close with a fizzing half-volley after good build-up involving Logan and Rooney.
But the second goal did come after the hour mark, and it was of Hearts' own making.
Anastasios Avlonitis seemed to have everything under control as he mopped up at the back but with Hayes closing fast, the defender mis-hit his reverse pass to goalkeeper Jack Hamilton, allowing the Irishman to intercept before rounding the keeper and sliding home.
From there it seemed to be a question of how many the Dons would score, and McLean forced Hamilton into a good save with a well-struck snap-shot from fully 30 yards.
Hayes could have bagged himself a second as he weaved his way into the area before lashing a fierce strike towards goal, but Hamilton was again equal to it.
The win delayed Celtic's title coronation until at least the end of the month but a good day was spoiled somewhat for the Dons when substitute Stockley was sent off in the final minute
Having been pulled back by Krystian Nowak, he caught the defender with a swinging arm and had no complaints as referee Steven McLean flashed the red card.
Source : PA