Kevin Cassidy emerged as the Donegal hero at Croke Park as the Ulster champions booked their place in the All-Ireland semi-final in sensational fashion.
The Gweedore man rifled over a stunning winning point in stoppage time at the end of extra-time, to finally settle a gripping encounter.
A 1-12 to 0-14 win sets up a last four meeting with either Dublin or Tyrone, their reward for reaching the semi-finals for the first time since 2003.
Three Eoghan O'Flaherty points helped the Lilywhites open up a 0-5 to 0-3 lead at the break. Substitute Christy Toye netted with his first touch on 58 minutes, but O'Flaherty sent the tie to extra-time.
Kildare led by 0-13 to 1-8 midway through, but Kevin Cassidy's superb long range winner in stoppage time sent the Ulster champions through to the last four.
Tyrone powered to a 3-19 to 1-14 win over Roscommon at Croke Park to set up an All-Ireland quarter-final clash with Dublin next weekend.
Sean Cavanagh's spectacular return to form was the catalyst for a Red Hands display which has shortened their odds for the Sam Maguire Cup.
Cavanagh hit a 2-3 tally in a man of the match display in this round four Qualifier clash, with Mark Donnelly also hitting the net for the Red Hands.
Two goals in the space of a minute set the game alight, with Cavanagh cancelling out Karol Mannion's 27th-minute strike.
Cavanagh's 1-3 helped Tyrone to a 1-9 to 1-8 interval lead, and they pulled away in ht final stages, killing off the Rossies' challenge with Cavanagh's second goal and a third from Donnelly.