Delegates rejected calls to back devolved management from leading party figures, including Janet Law, education convener in the SNP-controlled Perth and Kinross Council and national spokesperson on education.
Opposing a motion on approving devolved schemes that are "properly regarded and funded", Graham Sutherland, a secondary teacher and prospective parliamentary candidate in Edinburgh West, argued: "Devolved school management is a Tory Trojan horse set up to destroy comprehensive education."
The SNP, he said, needed to win the votes of teachers, traditionally Labour supporters, and rejecting DSM would ensure the party was not seen to back Tory policies.
"DSM creates extra stress, increases workload and detracts from teaching in the classroom. It is a dirty word," Mr Sutherland, a member of the Educational Institute of Scotland's local association in Edinburgh, told the conference.
He was backed by Rachel Martin, a Musselburgh primary teacher and EIS representative, who pointed out that headteachers of small primaries had similar amounts of administration to other heads but only two days of non-class contact time. Heads were "drowning in paper". She favoured an optional DSM scheme.
But Mrs Law argued: "DSM schemes were feared as a means of weakening the comprehensive education system but we have subverted the Tory agenda and turned it to our advantage." Teachers, unions and authorities had to work together to ensure the "fragile system" worked even better.
Jim Towers, spokesman on education in Aberdeenshire and prospective candidate in Aberdeen South, said devolved management was "unique" in education, "a good idea to emerge from the Tory think-tank". Mr Towers, who chaired the former Grampian Region's working party on DSM, said: "Yes, it does involve extra work for the teachers but the problem is the Tories. They have not funded it properly."
Proposing the pro-DSM motion, Phil Ellis, an Inverness secondary teacher and a primary school board chairman, said devolved management allowed schools to set priorities and address their own problems. If it was properly funded it offered "meaningful democratic opportunities".
Three SNP-run authorities in Moray, Perth and Kinross, and Angus are currently implementing devolved management schemes.