Derry looked well in control after Benny Heron’s 45th minute goal put them two points ahead.
But Quigley toe-poked the ball home at the near post in the 65th minute to keep the home side in the hunt for a semi-final place from Section B.
Derry lost forward Daniel McKinless to a black card for tripping in the 29th minute of a laboured first half.
Fermanagh led 0-3 to 0-1 after 10 minutes, Eamon McHugh and James McMahon with stylish, well-worked scores. Both sides struggled for fluidity but Derry drew level with two points inside a minute from midfielders Mark Craig and Mark Lynch.
Lynch then edged them into a slender half-time lead.
Heron jinked inside his marker to blast the ball to the roof of Fermanagh’s net, but the Oak Leafers didn’t register a point in the second half until corner back John O’Kane popped up in the 58th minute.
Points from Paul McCusker and Declan McCusker kept Fermanagh in touch before Quigley struck. Aidan Breen’s point sealed the win.
Scorers for Fermanagh: S Quigley 1-3 (3f), J McMahon, D McCusker, P McCusker, R Jones, E McHugh, A Breen 0-1 each
Scorers for Derry: B Heron 1-1 (1f), M Lynch 0-3 (1f), M Craig 0-2, J O’Kane 0-1
FERMANAGH: C Snow; N Cassidy, J Allen, B Mulrone; D McCusker, J Duffy, J McMahon; R Jones, R O’Callaghan; E McHugh, R Corrigan, P McCusker; C Flaherty, S Quigley, T Corrigan.
Subs: C Jones for Flaherty (HT), C Quigley for McHugh (46), A Breen for Duffy (53), E McManus for T Corrigan (53), M O’Brien for D McCusker (56), D Kille for O’Callaghan (63)
DERRY: T Mallon; O Duffy, N Holly, J O’Kane; K Johnston, L McGoldrick, B Óg McAlary; M Lynch, M Craig; SL McGoldrick, S Brady, B Heron; N Loughlin, D McKinless, D Heavron.
Subs: T O’Brien for McKinless (BC, 29), C McAtamney for Lynch (55), N Toner for Loughlin (55), C Murphy for Brady (56), D Brown for McAlary (68), J Kearney for L McGoldrick (70)
Referee: Joe McQuillan (Cavan).