VICENTE BESUIJEN was the two-goal hero as Aberdeen wore down obdurate Annan after an almighty scare.
Jim Goodwin’s side have been scoring for fun lately but could only muster one in 90 minutes as they were dragged into extra time by their League Two hosts.
Only when fatigued kicked in did the top flight team draw away and score four to make their passage into the last eight safe but far from comfortable.
Steven Swinglehurst’s powerful header deservedly gave Peter Murphy's men a late leveller and made it a long old day for the 1000-strong travelling support.
After scoring four and five respectively against top flight St Mirren and Livingston following a 12-goal group stage spree, this was about Aberdeen finding a different way to win.
Annan raised their game to unprecedented levels here. Chris Johnston was a constant, lively menace.
The ex-Kilmarnock winger cut in from the right to set up Benjamin Luissint who dragged his shot half a yard shy.
Home skipper Swinglehurst cleared a heavily deflected Matty Kennedy drive off the line with keeper Greg Fleming wrong-footed.
Shayden Morris blazed wildly over after fine footwork crafted him penalty box space to shoot.
Such room was at a premium for Aberdeen and Annan enjoyed plenty of it on the counter.
Tommy Muir was denied by the woodwork after winning the battle to meet Cammy Williamson’s flag kick.
Goodwin went for wing changes at the break as Jonny Hayes replaced Kennedy and Morris made way for Luis Lopes.
From Hayes, an instant impact. The veteran had a penalty claim denied when Lewis Hunter’s arm blocked his cross and, a minute later, Fleming clawed his chip shot off the line.
Luissant’s half volley drew Kelle Roos into sharp reactions and a good hold but Hayes was intent on putting matters right.
He dashed down the left and his delivery into the heart of the goalmouth was bundled across the line - just - by Besuijen.
The Dutch winger relish greater freedom. Jayden Richardson skimmed the crossbar from 20 yards after Besuijen’s set up. It was a dig he soon wished he’d kept a few inches lower.
For Annan never gave up. Roos kept his composure to clutch a close range Muir header first time.
But with 10 minutes left Swinglehurst rose to bullet home an equaliser from Johnston’s corner and gave Aberdeen it all to do again.
Besuijen went close with a minute to go but with Miovski withdrawn on 78 minutes for Ryan Duncan, their chief goal threat was on the bench for the remainder.
Ross McCrorie fluffed a chance off-balance six yards out but the rescue act was on the way.
Lopes stole across to the near post to meet Leighton Clarkson’s corner and glance home.
Still, Annan kept going. Muir laid a chance on for Luissint and Roos reached full stretch to save.
Aberdeen needed at least another - and got it on 105 minutes. Besuijen’s skills crafted some space down the left for him to curl a right foot finish beyond Fleming.
Annan completely wilted as Clarkson’s energy and skills floored two defenders and he tucked home the fourth.
