Gavin Rae netted Aberdeen's first goal at Pittodrie this season after six minutes before the in-form Michael Higdon equalised for the Steelmen from close range after 42 minutes.
Defender Shaun Hutchinson headed Well in front three minutes after the break before Nicky Law looked to have ensured victory with eight minutes remaining.
However Dons substitute Niall McGinn headed home two minutes later to set up a rousing finish with Northern Irishman Magennis netting the equaliser to deny Motherwell a three-point lead at the top of the Clydesdale Bank Premier League table.
Russell Anderson kept his place in the Aberdeen defence after successfully appealing the red card he was shown against Inverness as Craig Brown stuck with the same XI that started in last weekend's 1-1 draw.
Motherwell made only one change from the side that came from behind to beat Dundee 2-1 with Estonian attacker Henrik Ojamaa preferred to Jamie Murphy, who had to settle for a place on the bench.
Aberdeen's profligacy in front of goal had seen them draw 0-0 in each of their first three home matches of the new SPL campaign but they finally ended their scoring drought after only six minutes of this encounter.
Ryan Fraser and Stephen Hughes combined for a quick corner and found the unmarked Jonny Hayes on the edge of the box. The Irishman initially slipped before regaining his composure to float the ball onto the head of Rae, whose deft flick nestled into the corner of the net.
Motherwell looked for an immediate response to the early setback with midfielder Nicky Law twice going close from distance before Fraser Kerr headed over from a Tom Hateley corner.
The Motherwell pressure continued after 25 minutes when Ojamaa manufactured a yard of space for himself on the edge of the area before unleashing a low drive which was pushed away by Jamie Langfield.
Amid the barrage of Motherwell attacks, the Dons had a chance to double their advantage when Hughes cut the ball back for the diminutive Fraser but the teenager's header was easily saved by Darren Randolph.
But the Well equaliser arrived three minutes before the break when the Dons defence failed to deal with a Steven Hammell free-kick and, although Langfield managed to initially thwart Kerr's close-range effort, he was helpless to prevent Higdon turning the ball into the unguarded net for his seventh goal in four games.
And the visitors were in front within three minutes of the restart when Hutchinson rose highest to head home a Hateley corner to the delight of the visiting support.
Ojamaa could have put the game out of Aberdeen's reach when he was sent through by another perfectly-weighted pass from Hateley but Langfield managed to keep out the Estonian's drive at full stretch.
Aberdeen threw on McGinn and Isaac Osbourne for Scott Vernon and Rae after 63 minutes as they looked to get back on level terms but it was the visitors who looked the more dangerous with Chris Humphrey skipping past two defenders before seeing his eventual shot deflected kindly into the arms of Langfield.
The visitors had a strong claim for a penalty turned down with less than 15 minutes remaining when Law looked to have been pulled back by Osbourne, but referee Bobby Madden waved play on.
But the decision looked to have been rendered irrelevant when Well notched a third after 82 minutes, again courtesy of a Hateley corner which was flicked on by Kerr to Law who forced the ball over the line.
However, the Dons set up a dramatic finish when substitute McGinn headed home from a Fraser cross two minutes later and the comeback was complete when Magennis turned home an Andrew Considine shot deep into injury time.