The last eight draw, made at St Brendan’s Park in Birr on Saturday afternoon, threw up another big city clash after the counties were drawn together in the senior hurling and football championships.
Elsewhere, Connacht champions Galway have been paired with Tyrone, who beat Clare in Saturday’s round 2 qualifier.
Laois, comfortable winners against Meath, play Ulster champions Monaghan and Munster champions Kerry face Mayo, who put five goals past Westmeath on Saturday.
Cork survived a stern test of their credentials before edging past Armagh with just a point to spare at St Brendan’s Park in Birr.
Cork, who welcomed back Juliet Murphy at half-time, led 0-10 to 0-3 at the interval but they were left hanging on for a 0-16 to 2-9 win.
Second half goals from Kelly Mallon and Caroline O’Hanlon brought Armagh back into contention before player of the match Geraldine O’Flynn steered Cork home.
O’Hanlon had a late chance to level the game for Armagh, who had hit the front in the final quarter, but her free dropped short and Cork survived.
Elsewhere, Laois gained revenge for their Leinster semi-final defeat to Meath with a comfortable 1-14 to 0-7 victory over the Royals in Birr.
Tracey Lawlor scored 0-7 and Ciara Burke, captain of the Laois team that won the All-Ireland Minor B championship last Monday, scored the first half goal.
Laois led by 1-9 to 0-2 at half-time and were never troubled in the second half.
At Pearse Park in Longford, Cora Staunton hit 4-8 for Mayo as they beat Westmeath by 5-11 to 0-11.
Goals from Lisa Cafferkey and Staunton in the opening five minutes set Mayo on their way to a big win.
Staunton had a hat-trick by half-time as Mayo led by 4-7 to 0-4 at the break.
In the second game in Longford, Tyrone earned a hard-fought 1-15 to 1-9 victory over Clare, Cathy Donnelly with a late goal.
Scorers for Cork: V Mulcahy (0-6, 3f), G O’Flynn (0-3, 2f), D O’Sullivan (0-2), B Corkery, N Cleary, O Finn, C O’Sullivan & R Ní Bhuachalla (0-1 each).
Scorers for Armagh: C O’Hanlon (1-3), K Mallon (1-1), F McKenna (0-2), S McCleary (1f), M McGuinness & S Mackle (0-1 each).
CORK: M O’Brien; A.M. Walsh, B Stack, D O’Reilly; B Corkery, Angela Walsh, G O’Flynn; Annie Walsh, R Buckley; N Cleary, D O’Sullivan, O Farmer; V Mulcahy, C O’Sullivan, O Finn.
Subs: J Murphy for O Farmer, E Farmer for Mulcahy, S Harrington for Buckley, R Ní Bhuachalla for Finn, S Kelly for C O’Sullivan.
ARMAGH: K Daly; L Kenny, C Morgan, S Marley; S Reel, N Marley, N Henderson; C O’Hanlon, S McCleary; M McGuinness, F McKenna, M Tennyson; C Malone, K Mallon, M McAlinden.
Subs: S Mackle for Kenny, C O’Hare for Mallon, A Hughes for McGuinness.
Referee: S Joy (Kerry).
Round 2 qualifier
Mayo 5-11 Westmeath 0-11, Tyrone 1-15 Clare 1-9, Cork 0-16 Armagh 2-9, Laois 1-14 Meath 0-7.
Mayo v Kerry, Tyrone v Galway, Cork v Dublin, Laois v Monaghan.
Fixtures (venues and times, TBC)
Saturday, August 17: Galway v Tyrone, Monaghan v Laois; Saturday, August 24: Dublin v Cork, Mayo v Kerry.