In the latest twist in the Rangers power struggle, a senior judge said there was "no valid legal reason" for the club to block proposals for change at Ibrox.
Mr Murray, who led a failed Blue Knights takeover bid before Rangers oldco went into liquidation, won an interim interdict at the Court of Session in Edinburgh which stops the club's planned annual general meeting (AGM) from going ahead on October 24.
Mr Murray wanted the meeting delayed after the Rangers board blocked his AGM motion to have an election on the proposed admission to the board of himself, former chairman Malcolm Murray and his supporters Scott Murdoch, a director and managing partner of Loch Lomond Golf Club and Alex Wilson, a former human resources director with BT.
Lord Tyre, a former President of the Council of Bars and Law Societies of Europe, ruled there was no valid legal reason for Mr Mather and the other Rangers directors not to present Mr Murray's motion to the rest of the club's shareholders.
The court defeat was the second embarrassment for the Rangers board after they were earlier forced to publish amendments to weekend statements which suggested former Rangers director, South African businessman Dave King, had been lined up as chairman to lead a new fundraising bid.
Mr Murray said: "I think both Craig Mather and Brian Stockbridge have to seriously consider their positions because I think they are untenable. If this is the way the club is being managed then quite frankly there are real issues here."
The former Deutsche Bank executive added: "Today was really all about shareholder democracy. We wanted to put in front of the shareholders, the fans and other stakeholders the ability to have a democratic vote at the AGM.
"This is a democracy, you have to give people the chance to vote, and I can't see what the problem with this is."
Mr Murray, who was awarded costs, claims he has already turned down an offer from Mr Mather that would have seen him join a new-look board alongside Mr King - but only if he had dropped his legal action and walked away from a partnership of dissenting shareholders including leading Scottish businessman and entrepreneur Jim McColl.
He said his group has executives including former Liverpool managing director Christian Purslow identified who could step into key positions at Ibrox quickly and was supportive of having Mr King in the Ibrox boardroom. Rangers must now give 21 days' notice to shareholders before they can stage a fresh AGM.
Richard Keen, QC, representing the shareholder group, accused the club of engaging in guerrilla warfare in its battle to prevent the shareholders from joining the Ibrox board.
He told Lord Tyre the directors of the club had "committed an offence" by not informing other shareholders of the requisition.
He said: "An offence has been committed by every member of this board. The board have placed themselves in a very difficult situation by failing to discharge their statutory obligations.
"They have committed an offence. If I am right, the consequences of that must be visited upon them."
The Murrays, along with shareholders Ian Cormack, John Graham and Colin Howell, made requests in writing to Rangers International Football Club plc to give notice to members of the resolutions to appoint new directors at the AGM on September 27.
The shareholders' resolution for Ibrox change was denied when the board claimed it was not "validly executed".
A Rangers spokesman insisted after Lord Tyre's ruling the directors had been obliged to "seek further clarification" from the shareholders. He added: "Every effort was made to engage with the petitioning shareholders on these issues however these shareholders chose to resolve the matter in court.
"The company will now be taking steps to fix an alternative date for the AGM as soon as possible and for the business to be considered at the AGM to include the resolutions proposed by the petitioning shareholders."
Earlier Rangers released a follow-up statement to the London Stock Exchange claiming Mr King's published desire to become chairman did not relate to the board of the club owners Rangers International Football Club plc, which is on the Alternative Investment Market, but to a subsidiary board.