In the first half, Martin scored three times.
The League Cup final will be held in front of new Ibrox manager Giovanni van Bronckhorst after Martin Boyle's incredible first-half hat-trick stunned Rangers.
In 29 minutes, he scored from a corner, a fine finish and a penalty past Allan McGregor.
Scott Arfield gave Rangers a chance at the end of the first half, but they failed to test Matt Macey in the second.
It is a miserable start to the new era, with Van Bronckhorst expected to take control on Monday, but domestic finals were something the recently-departed boss struggled to reach.
In the last nine attempts, Rangers have only advanced to the semi-finals of the two cup competitions once.
Hibs had three heartbreaking losses at Hampden last year, but this statement win exorcised their demons.
They will face Celtic in the domestic final at the national stadium on December 19th, having lost the Scottish Cup final to St. John's.
Reaction as it happened.
Van Bronckhorst is watching a display.
As Van Bronckhorst looked on from the south stand, his eyes were fixed on Hibs.
Questions have been asked of Ross in big games after three defeats at the national stadium last term - one to Hearts in the Scottish Cup semi-final and two to St Johnstone in the League Cup last four and Scottish Cup final.
It was the first time since Hibs' 2016 Scottish Cup final win that these two have met, and Ross' men would have to show the spirit of Alan Stubbs' cup-winning side to prevent Rangers progressing.
It was the Leith side's first game in almost a month after a Covid outbreak and the international break, and signs of rustiness were obvious from the off as Paul Hanlon and Joe Newell were booked inside three minutes.
The only signs of impairment after that were from Rangers. Kevin Nisbet won a corner and the delivery hit James Tavernier and fell into the path of Boyle, who scored the opener.
Rangers were looking for a rapid response. The finish was not great, but Joe Aribo slipped in Morelos.
Nisbet played the Australian international through to drill emphatically low past Allan McGregor, and then showed the Colombian how it was done up the other end.
Rangers looked a threat in attack when Arfield had an effort parried away and another missed the target, but they still looked a shadow of their former self.
Hibs were in dreamland on 38 minutes if they weren't already. After Steven Davis tripped him in the box, he picked himself up to complete his hat-trick.
While their fans tried to figure out whether they were in a nightmare or not, Rangers grabbed themselves a lifeline when Arfield swept in a close-range finish with his left foot after Ryan Porteous failed to clear.
Ross was one of the men who just watched his team concede an equalizing goal. He will know how important that moment was as Rangers tried to get a second, with Leon Balogun and Connor Goldson heading wide.
The second-half spark from the Scottish leaders did not materialise. There was a lack of seriousness and with every backpass there was groans from their support.
Substitute Ryan Jack struck narrowly wide, before Macey almost set up a nervy end when he miscontrolled a pass and saw his touch go behind him and clip a post. It's proper heart-in-mouth stuff.
Every Rangers fan would have felt the same way as Van Bronckhorst sat with his hand over his face after Goldson flashed over a sitter.
The man of the match was Martin Boyle.
You can't look past the performance of the man who is now on 16 goals this season, after a devastating first-half performance was coupled with relentless running in the second period.
What did we learn?
Welcome to the world of football management. The new boss is going to have a lot to ponder on his first day.
It was hard to believe that a side was four points clear of the pack. In the entire league campaign, Rangers conceded 13 goals, but they shipped 23% of that figure in the first half.
The group are capable of rousing themselves if the Dutch coach demands a response from them in the Sparta Czech tie.
This result is remarkable for Hibs, but they haven't played in 25 days.
The result will go a long way in deflating the doubts surrounding Ross' big-game mentality, as he was questioned following last season's Hampden disappointment.
What's next?
Rangers will play Sparta Prague in the Europa League on Thursday, and Van Bronckhorst will be in charge. Next Sunday is when a trip to Livingston will take place.
Hibs play their rearranged league fixture at Ross County on Wednesday before travelling to St. John's on Saturday.
The Rangers are a team.
Hibernian
Line-ups.
Match statistics.
Live text.
Formation 4-3-3.
2Tavernier6Goldson26Balogun31
McGregor is a person.
2Tavernier
6Goldson.
Substituted for Basseyat for 80 minutes.
Booked at 83 minutes.
Substituted forHagiat 69' minutes.
10Davis
Substituted forWright in the 80's.
Substituted forJack at 69' minutes.
20 Morelos.
Substituted forSakalaat 61' minutes.
Substitutes.
3Bassey.
4Lundstram
7Hagi.
8Jack.
16Patterson
22Bacuna.
23Wright.
30Sakala
McLaughlin is 33
Formation 3-6-2
Campbell-Hayes and Doig are two people.
1Macey
6McGinn
Substituted forMcGregorat for 80 minutes.
The book was written at 1 minutes.
27Cadden.
22Doyle-Hayes.
Campbell
The book was written at 3 minutes.
Substituted for Stevenson at 59' minutes.
Substituted for Doidgeat 81' minutes.
10 Boyle.
Substitutes.
8Wright.
9Doidge.
13Gogic
Stevenson is a person.
19 Gullan.
21Dabrowski
Allan
24McGregor
25Scott.
The match ended with Rangers defeating Hibernian 3 to 3.
Rangers won the second half by a score of 1.
Scott Wright won the free kick.
Foul by Jake.
Foul by Christian Doidge.
Steven Davis won a free kick.
An attempt was missed. The shot from the centre of the box is too high forConnor Goldson. Alfredo Morelos assisted by a corner.
Corner, Rangers. Paul Hanlon was in the match.
An attempt was missed. Fashion Sakala's left footed shot from the left side of the box misses to the right. Steven Davis assisted.
Corner, Hibernian. Ianis Hagi Conceded.
Ianis Hagi of the Rangers had a foul.
Chris Cadden won a free kick.
Borna Barisic is shown with a yellow card.
An attempt was missed. The centre of the box is close, but Goldson misses the right. A cross is following a corner.
Corner, Rangers. Paul McGinn was in the match.
The substitution was for Hibs. Kevin Nisbet was replaced by Christian Doidge.
The Rangers had a substitution. Scott Wright is the new person.
The Rangers had a substitution. Calvin Bassey is the new replacement for Leon Balogun.
The substitution was for Hibs. Ryan Porteous was replaced byDarren McGregor because of an injury.
The attempt was saved. The ball is saved in the bottom right corner. Ryan Jack assisted.
