St Johnstone’s hopes of another cup final were dashed at Tynecastle.
In a tense and for the most part, closely-fought contest, Hibs edged the last four tie with a goal fit to win any semi-final.
Joe Shaughnessy had cancelled out a controversial Hibs penalty in the first half.
But, with both sides threatening a winner, John McGinn came up with a spectacular 20-yard strike mid-way through the second period to send Saints out of the cup.
The big team news was that all three of the Saints injury doubts started Dave Mackay, Murray Davidson and Chris Millar while Hibs’ new loan signing Anthony Stokes missed out with a back strain.
Hibs made the better start to the contest and Alan Mannus was tested with a couple of free-kicks that he dealt with well.
On nine minutes Mackay didn’t get enough on a clearance and McGinn narrowly missed the target with an 18-yarder.
Saints were struggling to get dangerman Michael O’Halloran into the game but they were able to release him with a ball over the top on 18 minutes, which produced a corner.
They tried a remake of the set-piece that resulted in a Simon Lappin goal at Ibrox, unfortunately somebody wasn’t on message this time and David Wotherspoon’s delivery found not a soul on the edge of the box.
Hibs took the lead on 29 minutes with a Jason Cummings penalty.
Liam Henderson won it when he went down under a challenge from Millar just inside the box. The Saints players were adamant that it was a dive but referee Steven Mclean had made his mind up.
It was probably a deserved lead, albeit a controversial goal, but Saints came back with the perfect response by equalising just three minutes later.
Wotherspoon crossed from the right and Shaughnessy produced a perfect looping header into Mark Oxley’s left-hand top corner.
There was a scary moment for the Perth men just before the break when Mannus dropped a corner, but luckily it fell at a friendly foot and Brian Easton cleared.
Hibs were on the front foot again after the re-start and Shaughnessy prevented them regaining the lead by blocking a goal-bound Cummings shot.
Saints got stronger as the game went on and on 63 minutes Lappin struck the crossbar with a wind-assisted free-kick that Oxley was nowhere near.
Hibs were still carrying a real threat though, highlighted by a 67th minute counter-attack that finished with Cummings shooting straight at Mannus.
Then seconds later a Chris Dagnall shot grazed the outside of the post.
It was an end to end game now, with Anderson having a shot charged down and Hibs hitting straight back with a Henderson run and shot.
And it was Alan Stubbs’ men who scored the decisive third goal on 74 minutes a superb low McGinn strike from 20 yards out.
McGinn should have finished the contest 10 minutes later but shot wide from close range.
Saints came close to grabbing an equaliser when a Liam Craig cross was just too firm for Steven MacLean to connect with at the back post.
And near the death Oxley kept out a Shaughnessy header from a Lappin corner.
But they couldn’t find a goal and went out of the cup.