The sides were locked at 2-2 after 90 minutes on Tuesday following Garry O'Connor's late equaliser, and were unable to add to the score in goalless extra-time at Fir Park.
Visiting goalkeeper Mark Brown saved from Jamie Murphy and then decisively from Nicky Law in sudden death, after home counterpart Darren Randolph had also saved a spot-kick from Callum Booth.
O'Connor had scored the first goal of the night for Hibs but saw it cancelled out before the interval by strikes from Keith Lasley and Michael Higdon.
Hibs carved the first scoring chance inside two minutes when Martin Scott bore through the centre of the Motherwell ranks and down on goal, passing to the right for the arriving Leigh Griffiths to have a shot.
The Hibs forward twice tried going for goal with early long-range efforts, then helped the visitors take a deserved lead on 19 minutes, sending a precise cross into the box for O'Connor, who neatly converted at the near post, sending it into the bottom right corner.
It could have been 2-0 just two minutes later when Griffiths received a long ball into the six-yard box and tried to loft it over Randolph, but the home goalkeeper stretched to make the save.
However, Motherwell immediately responded with their best spell of the game, a hat-trick of testing goalline crosses from winger Chris Humphrey at the heart of their reply.
The hosts were rewarded with a 29th-minute equaliser when Lasley struck from just inside the area, Higdon playing him the crucial pass following a Tom Hateley corner.
Law almost put Motherwell in front on 38 minutes, only to see his diagonal effort go narrowly wide of the right-hand post - but the Fir Parkers were in front one minute later when Law found Higdon at the end of an impressive one-touch passing move, allowing the forward to score with a neat sidefoot from the edge of the area.
Hibs were again to the fore as the second half got underway with Martin Scott having an opportunity to restore parity after five minutes, but Randolph stretched to parry his promising shot from inside the area and the loose ball was headed away from the approaching O'Connor.
Griffiths again tried his luck with a shot from outside the box which forced a save from Randolph at the left-hand post, and was again denied by the goalkeeper from six yards after slipping past Tim Clancy on the right.
Higdon had the chance to double Motherwell's lead just after the hour but headed over from a Humphrey cross.
Hibs thought they had equalised on 65 minutes after taking advantage of calamitous home defending but O'Connor saw his finish chalked off and was booked after referee Willie Collum spotted the use of a hand in the build-up.
The striker had another chance as the game entered its last quarter after linking in the box with newly-introduced substitute Junior Agogo as the visitors sought a late equaliser.
Victor Palsson's drive from outside the box was stopped by the stooping Randolph - but O'Connor equalised by running onto Griffiths' pass four minutes from time and slipping the ball low past the home goalkeeper.
Visiting goalkeeper Brown twice made saves from Law in the first half of extra time; Towell rolled an inviting ball right across the face of goal and Agogo tested Randolph with a strike which was beaten away at the right-hand post.
Lasley shot wide in the first minute of the second extra period and Motherwell team mate Murphy hit the side netting; while Griffiths' free kick at the other end was easily held. Robert McHugh had the ball in the net for Motherwell late on but was ruled offside ahead of the shoot-out.