It announced yesterday that the resolution was voted down after a single vote but after a request for a detailed breakdown of how bishops, clergy and laity voted, it was found that the two-thirds majority needed was actually met.
Though the next synod in 2019 needs to pass the resolution for it to become church law some Canadian bishops have already said they will begin performing them.
Bishop John Chapman of Ottawa told CBC: "It is time my friends. It is past time."
Ven Dr Michael Thompson, General Secretary of the Anglican Church of Canada general synod, said in a statement: "Today we discovered that the electronic voting system we were using miscoded my electronic file.
"I was listed, and my vote was counted, as a lay person instead of a priest. This one vote changed the outcome of resolution A051-R2—the resolution to amend the marriage canon.
"This vote has been difficult for many, and no outcome can address all of our church's need to live and work together.
"We have a long road ahead to restore our common life."
Archbishop Fred Hiltz, the primate of the Anglican Church of Canada, is expected to release a pastoral letter after the result on Thursday.
The Church's decision, which comes after the Episcopal Church of America passed a resolution allowing same-sex marriages earlier this year, will only increase divisions among the wider Anglican Communion - most of which holds that sexuality and marriage should be between a man and a woman only.