Both sides made two changes from their respective cup wins at the weekend, with Bruce Anderson and Connor McLennan dropping to the Dons bench to be replaced by Jon Gallagher and Lewis Ferguson. Well's two changes saw Liam Grimshaw and Donnelly replace Richard Tait and Christian Ilic.
With their league records showing not much between the sides, it was no surprise that the game was a closely-fought affair.
Indeed, it took almost 20 minutes for the visitors to fashion the first clear-cut chance, James Scott's angled drive beating Joe Lewis in the Aberdeen goal, only to be cleared off the line by the well-placed Shay Logan.
Logan was involved at the other end as his cross was flicked on by Sam Cosgrove to Andrew Considine at the back post. The experienced defender turned the ball towards goal, but goalkeeper Mark Gillespie saved with his feet.
Chances were at a premium, but Chris Long threatened to get in behind the Dons defence just after the half hour, only to be stopped in his tracks by a superbly-timed Dylan McGeouch challenge. The striker, though, sustained an injury which saw him replaced by Ilic.
It would be the visitors who broke the deadlock on the stroke of half-time as Liam Polworth's right-wing free-kick found Donnelly unmarked at the back post and he headed past Lewis from close range.
With the home support restless, a lack of second-half chances certainly did not help the mood around Pittodrie, and it was beyond the hour mark before Ash Taylor threatened the Motherwell goal, his header over the crossbar from Niall McGinn's corner.
Set pieces looked to be Aberdeen's best threat, and it was from another corner that Scott McKenna saw a near-post header blocked, before Considine volleyed the rebound over the bar.
With 10 minutes left the Dons went for broke with defenders Taylor and Logan replaced by strikers Anderson and Curtis Main, but though there was plenty of endeavour, they still struggled to create clear chances.
That being said, fellow substitute Ryan Hedges played a superb teasing ball across goal with five minutes remaining, but Cosgrove was unable to get on the end of it when it seemed any touch would lead to the leveller.
And as the home side piled bodies forward, Anderson was unlucky to see his volley blocked at the far post as Aberdeen's desperate attempts to take something from the game went unrewarded.