St Mirren were heading for the semi-finals after Paul McGowan capitalised on a sustained spell of pressure by slotting home from close range in the 77th minute at St Mirren Park.
The arrival of Michael Higdon and Kenny McLean and a tactical switch had turned the game in St Mirren's favour after the hour mark after Aberdeen had come out in determined mood following an uneventful first half.
Saints had several chances to kill the tie off but their habit of conceding late goals again proved costly as substitute McArdle hooked home following Paul Hartley's free-kick.
The Dons, with Chris Maguire back from suspension up front and Josh Magennis in at right midfield, pushed St Mirren back in the early stages as they responded to some noisy backing from a large travelling support, who had failed to be deterred by the morning snowfall.
But Craig Brown's side, with Steven Smith on the left of midfield in their 4-4-2 formation, failed to maintain their tempo after David McNamee went off injured for McArdle in the 13th minute.
St Mirren improved, with Darren McGregor back following the death of his father in a 3-5-2 formation, and the defender's header nearly fell for McGowan following a free-kick.
Aberdeen twice threatened around the half-hour mark, firstly when Rob Milsom's deep corner found Scott Vernon, whose header was diverted wide in a crowded goalmouth for another corner.
Hartley's delivery from the other side fell for Milsom on the edge of the box but his volley was inadvertently blocked by team-mate Nikola Vujadinovic.
Saints fought back again before Vernon glanced a header beyond the far post following Andrew Considine's cross.
Aberdeen produced the first on-target effort of note just after the break when Magennis unleashed a powerful 20-yard strike which took a slight deflection before being pushed away by the diving Paul Gallacher.
The Dons came close again as they controlled possession with Saints down to 10 men as John Potter received treatment to a head wound. Another forward burst by Magennis set up Milsom to curl just wide from 20 yards.
Higdon came on for Potter on the hour mark with McGowan dropping back into a new 4-4-2 formation but Aberdeen soon came close again when Hartley volleyed just over following a half-cleared free-kick.
There were more changes as both sides looked for a spark with Nick Blackman and Sone Aluko coming on for the Dons and McLean on for Jim Goodwin in the St Mirren midfield.
McLean almost made an instant impact in the 69th minute running onto Higdon's clever through ball, but Jamie Langfield came off his line to block with his legs before recovering to stop Higdon's follow-up.
Higdon curled just wide from long range before he headed against the underside of the bar following Steven Thomson's cross.
St Mirren kept up the pressure and they broke the deadlock when McGowan converted from close range after Higdon had volleyed back Dargo's deep cross.
Saints soon cut Aberdeen apart again when sharp passing from Higdon and McGowan sent Thomson down the right but Langfield was alert as McLean met the resulting cross on the half volley.
Zander Diamond headed Hartley's corner wide but Saints missed two clear chances to finish them off as Higdon miscontrolled after being played clean through before Dargo failed to round Langfield.
And St Mirren were made to pay more than three minutes into injury-time after McGowan fouled Maguire 35 yards out.
Hartley chipped in the free-kick and McArdle reacted to a flick-on to hook home from close range to set up a replay on Wednesday.