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.
As expected, goalkeeper Darren Randolph made an immediate return from suspension while Stuart Carswell started in midfield in place of Nicky Law. The absence of captain Russell Anderson for a back injury forced a defensive reshuffle for the Dons, but Randolph was the busier goalkeeper in the first half.
He held an early header from the recalled Fallon before Jamie Langfield saved from Carswell after the midfielder was found by Jamie Murphy. Higdon headed a Chris Humphrey cross off target before Murphy moved into the area and a clumsy Shaughnessy stumbled into his back.
A Jonny Hayes effort from long range had Randolph at full stretch. Aberdeen came close once more when Fallon's header forced a good save out of Randolph but the visitors took the lead six minutes after the restart as Niall McGinn crossed and Scott Vernon headed back across goal for Fallon to score with a precision volley.
There might have been a quick-fire equaliser, but ex-Well defender Mark Reynolds made a last-ditch tackle on Higdon as the striker tried to meet Stevie Hammell's cross.
The Dons continued to threaten as McGinn's shot was saved by Randolph, before McGinn played the ball back for Fallon, who had only Randolph to beat, but saw his shot met with a firm hand and McGinn's follow up was ballooned off target.
Motherwell failed to heed the warnings, but could do little about Aberdeen's second as they were cut open. Hayes raced down the left to the by-line and crossed low, right-back Shaughnessy racing to meet it for a simple tap-in.
Slowly Motherwell were coming back into the game and Shaun Hutchinson headed weakly at Langfield from a Keith Lasley free-kick. But they never looked like breaching the Dons defence until a penalty was awarded for handball against Clark Robertson. Higdon's spot-kick went in off Langfield but it was the final act as the Dons advanced.