The Dons had defender Joe Shaughnessy dismissed after 14 minutes at Fir Park but the home side were unable to make their numerical advantage count and were punished late on by substitute Considine and Hayes.
Motherwell had an early John Sutton goal ruled out for offside but they struggled to make their numerical advantage count during the first half.
The home side improved after the interval, with Stuart Carswell missing a good chance and Shaun Hutchinson seeing a header hit the goal frame.
However, they were hit with a double late whammy as Hayes crossed for Considine to head home, and Hayes then sealed victory with an injury-time strike.
Motherwell thought they had gotten off to a dream start when Sutton turned the ball home after a clearance cannoned off Paul Lawson, but linesman Graham Chambers raised his flag after a delay of several seconds.
The other major first-half decision also came during the early exchanges as Shaughnessy saw red for sliding in heavily on Zaine Francis-Angol.
Shaun Hutchinson was fortunate to escape with a yellow card for scything down Niall Ginn, but the first half finished scoreless as Motherwell were unable to break down Aberdeen's packed defence.
Motherwell had a penalty appeal turned down on 48 minutes when Mark Reynolds appeared to bring down Henri Anier, but the hosts were beginning to carve out chances.
Carswell could only shoot straight at Jamie Langfield after being teed up by Francis-Angol, while Hutchinson headed off the junction of post and bar from substitute Lionel Ainsworth's corner.
But Aberdeen remained a threat on the counter-attack and the hosts were caught napping with seven minutes remaining when Considine rose at the back post to head Hayes' delivery past Gunnar Nielsen.
Stephen McManus spooned a volley over as Motherwell pushed for an equaliser, but McGinn twice came close at the other end before Hayes netted with the last kick of the ball.