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.
The Dons will play at Easter Road in February, while Motherwell have to settle for playing Hibs in the Clydesdale Bank Premier League this weekend.
As expected, goalkeeper Darren Randolph made an immediate return from suspension and, in a second change from the side which beat Ross County on Saturday for Motherwell's first home win in three months, Stuart Carswell started in midfield in place of Nicky Law (ankle).
The absence of captain Russell Anderson (back) 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 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.
Murphy shot off-target when he cut in on to his right foot before a similar Jonny Hayes effort from long range had Randolph at full stretch.
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.
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 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.
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.
Meanwhile, Billy McKay's double was enough for Inverness to beat local rivals Ross County 2-1 on a sub-zero night at the Caledonian Stadium.
The 24-year-old has now scored seven goals in his last five games with his brace setting up a last 16 tie with Kilmarnock.
McKay fired home an early penalty before Iain Vigurs' sublime finish levelled things just before half-time, but a spectacular curler from the hosts' in-form striker settled things nine minutes after half-time.
The Highland neighbours met in the aptly named Cold Firm derby after sharing a thrilling 3-3 draw in Dingwall 10 days ago.
Inverness made no changes to the side which won 3-0 against Hibernian on Saturday, which sent them above the Edinburgh side into second in the league.
Influential midfielder Stuart Kettlewell replaced Gary Glen in the only change to the County side which lost 3-2 to Motherwell on Saturday.
Inverness started where they left off against Hibs and took a ninth minute lead. Former Inverness stalwart Ross Tokely was adjudged by referee Craig Thomson to have taken down Gary Warren in the area.
The freezing conditions soon saw the game deteriorate into a battle of attrition as both teams had spells on top but failed to carve out anything to threaten either goal.
No further chances were created until the 35th minute when Ross Draper found Doran just outside the area and the Irishman, making his 50th appearance for Inverness, shot inches wide.
It may have been a costly miss as County levelled four minutes before the break.
Staggies fans will not have minded waiting for their opportunity with Vigurs netting a beautiful equaliser.
The former Inverness midfielder dinked the ball over charging goalkeeper Antonio Reguero from 25-yards after he was found by Colin McMenamin.
Draper might have put the home side back in front on the stroke of half-time but he screwed his low piledriver just wide from Richie Foran's lay off.
County started brightly after the interval with Rocco Quinn forcing Reguero into a save, but moments later McKay netted his second of the game with a superb curling strike from just outside the box for his 13th goal of the season.
Vigurs had the opportunity to level the scores after 68 minutes when he connected with a Quinn cross but the close range header was straight at Reguero.
Seconds later County substitute Grant Munro watched as his header was cleared off the line by David Raven.
McMenamin was next to try his luck after being played through by Scott Boyd, but his low effort rippled the side netting.
County substitute Steven Ross headed a Mark Fitzpatrick cross just wide with seven minutes remaining an visiting captain Richie Brittain had the chance to grasp a last-minute equaliser but it was cleared by Josh Meekings.