New Zealand striker Fallon, scorer of both goals in the Scottish Cup quarter-final win at Fir Park last season, netted a sublime 51st-minute strike and 10 minutes later Joe Shaughnessy completed a flowing move with the second, his first for the Dons.
Michael Higdon's stoppage-time penalty was merely a consolation as Motherwell, the 2011 runners-up who had lost just once in 13 prior games against Aberdeen, tumbled out of the cup to the same opponents for a second successive season.
Darren Randolph held an early header from the recalled Fallon before Jamie Langfield saved from Stuart Carswell after the midfielder drifted into the area unmarked and was found by Jamie Murphy.
Motherwell pushed on, with Murphy and Chris Humphrey threats, but were unable to test Langfield again in the opening period.
Higdon headed a Humphrey cross off target before Murphy moved into the area and a clumsy Shaughnessy stumbled into his back.
The Motherwell winger stayed on his feet, meaning referee Willie Collum, the official who awarded a controversial penalty in Sunday's Dundee derby, was not required to grant another spot-kick. A penalty would surely have been the result had Murphy gone to ground.
Aberdeen came close once more when Hayes, who was lively throughout, and Clark Robertson combined down the left and the full-back crossed to the back post. Fallon headed goalwards, but Randolph saved well before scrambling clear at the feet of Niall McGinn.
The visitors took the lead six minutes after the restart following a disputed corner deep in their own half.
The ball was worked up the left, McGinn crossed and Scott Vernon headed back across goal for Fallon to pounce with a precision volley which found the top corner.
The Dons continued to threaten and Vernon played McGinn through, the striker shooting towards Randolph's near post as the goalkeeper saved.
Shaughnessy's shot from the resulting corner flashed narrowly wide before the Dons raced through the Well rearguard once more.
McGinn again was to the fore, playing the ball back for Fallon, who had only Randolph to beat. Fallon's shot was met with a firm hand and McGinn's follow up ballooned off target.
Motherwell failed to heed the warnings, but could do little about Aberdeen's second as they were cut open. Jonny Hayes raced down the left to the by-line and crossed low, right-back Shaughnessy racing to meet it for a simple tap-in.
Hayes' attempt at a cheeky chip did not pay off, but slowly Motherwell were coming back into the game and Shaun Hutchinson headed weakly at Langfield from a Keith Lasley free-kick.
Try as they might Motherwell never looked like breaching the Dons defence until a penalty was awarded for handball against Robertson. Higdon's spot-kick went in off Langfield but it was the final act as the Dons advanced.