Kildare trailed by nine points at half-time, but turned the tables to deliver a 2-18 to 1-16 win over Mayo at Ballina Stephenites.
Two second-half goals from Willie Greene paved the way for an away win, in a game where Mayo were strong in the opening half.
Aided by a strong wind, Mayo led by 0-07 to 0-04 after 29 minutes before Johnny Byrne saw red for the visitors.
Mayo could have been further ahead, but for a superb save by Paul Dermody after 20 minutes, with Kildare leading 0-04 to 0-03 at that stage.
However, the hosts then took control, with Kildare only managing one further point late in the half as Mayo powered to a 1-11 to 0-05 interval lead - dual player Keith Higgins netting a 34th-minute goal.
Kildare worked hard on the restart and, aided by the introduction of Gerry Keegan, Brian Lawlor’s side cut the gap to three points by the 44th minute.
A cracking goal by Greene ensured a 1-11 to 1-07 score-line, before Mark Delaney cut the gap further.
A second Greene goal arrived in the 47th minute to level the tie at 2-09 to 1-12.
Kildare moved 2-12 to 1-12 ahead at the end of the third quarter, before Mayo bounced back with Kenny Feeney blazing a penalty over the crossbar to cut the gap to the minimum.
However, Mayo only managed two further points, as Kildare stood firm to take a five-point win.
A late Paddy Henry pointed 65 earned Derry a semi-final place, thanks to a one-point 1-12 to 2-08 win over London in Owenbeg.
Derry were forced to dig deep after a strong London start, which saw the Exiles lead by 0-04 to 0-00 inside 14 minutes, with Michael Ivors among their scorers.
However, the Oak Leafers responded with Paul Cleary opening their account, a Ruairi Convery free levelling the game at 0-04 apiece after 23 minutes.
Scores were hard to come by thereafter, but London worked hard, with Mark O’Dwyer netting a goal just before the break to ensure the visitors took a 1-05 to 0-06 half-time lead.
Derry took control on the restart, a Paddy Henry goal helping them regain the lead, before extending their advantage to four points by the 48th minute.
London worked hard though as O’Dwyer bagged his second goal with eight minutes remaining to level the contest.
Niall Ferris and Peter Phelan swapped points, with extra-time looking likely.
However, Henry’s late point ensured Derry advanced to the last-four, with a quarter-final for London next weekend.
