The result -- confirmed by a sea of raised hands but no formally recorded vote -- meant Sinn Fein, once a hard-left party committed to a socialist revolution, has abandoned its decades-old hostility to law and order.
The vote, taken after daylong debate among 2,000 Sinn Fein stalwarts, represented a stunning triumph for Sinn Fein chief Gerry Adams, the former Irish Republican Army commander who has spent 24 years edging his IRA-linked party away from terror and toward compromise.
It strongly improved the chances of reviving power-sharing, the long-elusive goal of the 1998 Good Friday peace pact, by Britain's deadline of March 26.
"Today you have created the potential to change the political landscape on this island forever," Adams told the conference.
Earlier, many speakers said for decades they had dreamed of defeating the province's mostly Protestant police force and forcing Northern Ireland into the Irish Republic.
Some IRA veterans recalled beatings inflicted on them by detectives during interrogations. Others noted they had served long prison sentences for attacks on police, more than 300 of whom were killed during the IRA's failed 1970-1997 campaign.
But nearly all speakers said they were voting to dump their party's anti-police position for the sake of peace.
"This shows that the war is over. And if the war is over, we have to build the peace," Adams said in an interview during an earlier break in debate.
Other Sinn Fein leaders sought to cloak their vote in bellicose terms, arguing that their position as the major Catholic-backed party in Northern Ireland meant they would be able to tell police commanders what to do.
"We have to boss policing, because we are the bosses," said Sinn Fein's deputy leader Martin McGuinness, who according to police and the Irish government was an IRA commander from the early 1970s until last year.
McGuinness said the expected strong "yes" vote to policing wouldn't mean people in Sinn Fein power bases should be expected to welcome police into their communities.
"They're going to have to earn our trust. And we will let them know that they are going to be the servants of the people, not the other way around," McGuinness said.
At stake is the revival of power-sharing, the central goal of the U.S.-brokered Good Friday peace accord of 1998. A previous coalition collapsed in 2002 amid chronic Protestant-Sinn Fein infighting over the IRA's future.
Since then the Democratic Unionists, who represent most of the province's British Protestant majority, have insisted they will form a Cabinet alongside Sinn Fein only if Adams' party demonstrates support for law and order in areas where, from 1970 to 2005, justice often was administered with IRA bullets to the legs of petty criminals.
Crucially, however, the party motion approved Sunday commits Sinn Fein to begin supporting the police only after power-sharing is revived -- and only if the Democratic Unionists agree to transfer control of Northern Ireland's justice system, including the police, from Britain to local hands by May 2008.
The Democratic Unionists are refusing to make either commitment until they see Sinn Fein's behavior to the police change.
Democratic Unionist leader Ian Paisley said his stand had "forced Sinn Fein to recognize support for the police and the rule of law as an issue of paramount importance for which there can be no other way."
"Sinn Fein must now walk this road," said Paisley, an 80-year-old evangelist. "The time for true, visible and open support for the police and law enforcement has arrived."
In London, British Prime Minister Tony Blair welcomed Sinn Fein's shift, but said it was only the start of a critical period in peacemaking.
"The next few weeks will be as important as the negotiation of the original Good Friday agreement," Blair said.
Irish Prime Minister Bertie Ahern called Sinn Fein's vote "a landmark decision" that was "profoundly in the interests of everybody."
Chief Constable Hugh Orde, commander of the Police Service of Northern Ireland, said IRA supporters no longer had any valid reason to withhold support for his force, which is midway through a 10-year reform program as part of the Good Friday deal.
The reform effort, which has increased the force's proportion of Catholic officers from 8 percent to 20 percent since 2001, means people in Sinn Fein strongholds should feel free to telephone police when they see crimes happening, Orde said.
"We need to see some tangible outcome," he said.