Hayes settled a low-key encounter in favour of the Dons, who go fifth in the Scottish Premiership as a result, while Motherwell – for whom this was a fourth straight loss – remain 11th.
Aberdeen made an excellent an decisive start to the game, scoring after just 90 seconds when Hayes slotted David Goodwille’s pass past Motherwell keeper Dan Twardzik.
The goal came at the end of a good passing move and was a just reward for Hayes’ persistence under pressure from covering defenders.
Hayes almost had a second immediately afterwards but his chip over the goalkeeper was narrowly over the target too.
Twardzik then made a good stop from Goodwillie before Hayes’ cross eluded Niall MGinn in the box as the Dons looked to increase their advantage.
Motherwell’s best chance in the first half feel to Stephen McManus, who struck the bar with an instinctive effort after the hosts had failed to clear a corner.
Logan had a shot kept out soon after the interval after he met a right-wing cross but Twardzik collected it comfortably.
Goodwillie failed to make a clean connection at a scramble after a corner and then hammered a shot over the bar as Motherwell struggled to get into the game.
Defender Craig Reid had a low effort saved and McGinn was marginally wide with a first-time strike as the game entered its final 10 minutes.
It was to prove to be Motherwell’s last attempt as they succumbed to a fourth straight defeat in a game of few chances.