Hibs travel to Rangers on Saturday knowing victory would take them top of the table at least until Sunday amid talk they will never have a better chance of winning at Ibrox.
Their opponents have been through the wringer this week, having suffered arguably the most humiliating defeat in their European history, having been shamed by a "moronic" fan who racially abused Maurice Edu, and having lost key men Madjid Bougherra and Pedro Mendes to injury.
Notwithstanding Rangers' recent troubles, neither of the Old Firm have managed to set the SPL alight this season, leading some to predict at least one of them could finish outside the top two for the first time since 2006.
And Murray believes third-placed Hibs could be the side to break them up.
"I think we all look to get into that elite group," he said.
"It's normally Rangers, Celtic, who are always up there challenging each other.
"If one of us can maybe get ourselves amongst it - like Hearts did a couple of years ago - it would be great; not just for the team that gets there, but for the rest of the teams in the league, to show that it can be done.
"We can talk about it every day and for the next two or three years. If nobody does it, it'll be the same old story."
Having spent two years at Rangers in between his two spells at Hibs, Murray knows the post-mortem into Tuesday night's 4-1 thrashing at the hands of Unirea Urziceni will have been long and painful.
"It was a poor result; I think everybody knows that," he said.
"This is the time where you'll see who the real leaders are in the Rangers team.
"I would say they're missing Barry Ferguson.
"But there's a chance for others now to step up to the plate and I'm sure they will."
He added: "You look around their changing room, and they've got some good players and big players.
"They've got Mendes, Bougherra and Davie Weir.
"They've got big players with big reputations; they've been in tough situations before and I'm sure they'll pick themselves up."
The 28-year-old hopes the malaise continues for at least another 24 hours but fears Rangers may have used up all their bad luck on Tuesday.
"You don't become a bad team overnight," he added.
"Everything went right for the Romanian team and whatever could go wrong for Rangers did go wrong."
Murray endured similar days during his ill-fated time at Rangers, not least against Hibs, who twice won 3-0 at Ibrox in games he started.
He has been less successful there as part of a visiting side and believes the key to any team breaking the Old Firm's stranglehold on Scottish football is beating both of them on a regular basis.
"I've been to Ibrox and I've been hammered before; I've been to Ibrox and had results before," he said.
"But it's getting it down on a consistent basis, going to Rangers one week and going to Parkhead the next week and coming away with points."
Asked about the morale in the Hibs camp on the back of 10 points out of 12, Murray said: "We are confident because we're playing well.
"But that can turn very quickly if you don't keep the results going."