Cluxton, who is due to captain his country, is putting his club first and his superb second-half save from Darren Clarke ensured Parnells an 0-11 to 1-8 draw after 60 minutes.
Niall Collins goaled for the Coolock men after five minutes of extra-time and the accuracy of both Armagh senior John Murtagh and Laois native MJ Tierney saw Parnells home with six points to spare.
Elsewhere, goals by Ciaran Dorney, Tomás Quinn, Padraig Lee and Diarmuid Connolly helped St Vincent’s to a facile 4-11 to 1-2 win over UCD in O’Toole Park.
On Saturday afternoon, Bernard Brogan inspired St Oliver Plunkett’s/Eoghan Ruadh to a comfortable 1-14 to 0-7 win over a limited O’Toole’s at Parnell Park.
Brogan, missing younger brother Alan who was out through injury, kicked four superb points from play in the first half as Plunketts eased to a 0-9 to 0-2 interval lead.
O’Toole’s battled gamely throughout, with midfielder Michael Healy landing four points over the hour, but they were never likely to produce a shock result and their fate was sealed when Brogan accepted a pass from Jason Sherlock to score the game’s only goal in the 56th minute.
Holders Kilmacud Crokes were dumped from the championship as St Brigid’s gained revenge for last year’s county final loss as they registered a 0-8 to 0-7 victory.
Mark Vaughan kicked three glorious points from play in an opening half dominated by Crokes and their lead would have been greater than 0-4 to 0-2 but for two sublime saves by Shane Supple in the Brigid’s goal, denying both Vaughan and Barry O’Rorke.
It was a different tale upon the restart as Brigid’s assumed complete control at midfield, with scores from Ken Darcy, the excellent Mark Cahill, Ken Kilmurray and Paddy Andrews confirming their quarter-final berth.