Kenny McLean had a chance to level before the interval, but his headed effort forced another save from Long, ensuring that Motherwell remained in front at half time.
The home side needed just two minutes to add another as Adam Rooney won the ball back on the edge of the box just moments after missing another chance, this time powering it past the keeper to put Aberdeen ahead.
Motherwell rallied as they to tried to find a quick equaliser and halt Aberdeen's run, but McDonald and Erwin both forced saves from the keeper.
However, Aberdeen soon started to dominate possession again as they tried to put the win beyond doubt, but Peter Pawlett was denied as he unleashed a long-range effort, while David Goodwillie fired just wide.
Lionel Ainsworth had a last-gasp chance to rescue a point for the visitors, as he cut inside before attempting to curl the ball in from the edge of the box, but his finish failed to trouble the keeper.
The win keeps Aberdeen second in the table, three points behind leaders Celtic, while Motherwell remain in the relegation playoff spot.