The ex-Blue Knight has been handed an interim interdict blocking the meeting taking place on October 24 at the Court of Session in Edinburgh.
Murray wanted the meeting delayed after the Rangers board blocked his motion to have an election on the proposed admission to the board of himself and former chairman Malcolm Murray, as well as allies Scott Murdoch and Alex Wilson, added to the business of the AGM.
Lord Tyre ruled there was "no valid legal reason" for chief executive Craig Mather and the other Rangers directors not to present the Murrays' motion to the rest of the club's shareholders.
Rangers must now give 21 days' notice to shareholders before they can stage a fresh AGM.
Murray was also awarded costs for Monday's hearing.
The Rangers board was accused in court of engaging in "guerrilla warfare" in their battle to prevent the group of shareholders from joining the Ibrox board.
It was also claimed that the directors may have broken the law by failing to tell the rest of the club's shareholders about the bid in enough time before the scheduled AGM.
Lawyer Richard Keen QC, representing the shareholder group led by the two Murrays, told Lord Tyre that 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 current Rangers board had claimed their application for a vote was not properly authenticated and did not arrive on time.
Paul Murray was in court on Monday morning to hear Mr Keen, Dean of Faculty of Advocates, claim the board had "engaged in guerrilla warfare in respect of the requisitions".
He claimed the signatures requested by the board had been offered "timeously" before adding: "These requests have been sent by the relevant companies and on the face of it there is no reason to doubt their validity."
Heriot Currie QC - representing the board of Rangers International Football Club - told Lord Tyre: "The petitioners have known since September 12 that they had to organise themselves for a shareholder meeting by no later than October 30."
The court defeat was the second embarrassment for the Rangers board on Monday after they were forced to publish amendments to weekend statements which suggested Dave King had been lined up as chairman and would lead a new fundraising bid.
Rangers released a follow-up statement to the London Stock Exchange claiming that King's position would be on the football club board, chairing the company formerly known as Sevco Scotland, and not the plc board, which has been without a chairman since Walter Smith stepped down.
The club, who last month announced an operating loss of £14.4million, said: "At the insistence of our nominated adviser, the board needs to make it clear, for regulatory reasons, that the board of directors referred to above is The Rangers Football Club Limited, the wholly owned subsidiary of The Rangers International Football Club PLC.
"Although we welcome the support of Dave King, no decision has been made to appoint him as a director. There are regulatory matters which would need to be resolved prior to any such appointment.
"The directors also expect that in the medium-term future, possibly coinciding with the return to top league football in Scotland, it may be in the best interests of the company to raise further capital.
"However, there is no requirement for short-term funding, and as such neither the company nor RIFC are actively seeking finance. Nonetheless, we are committed to exploring a future involvement by Mr King in the club."