The Deputy First Minister branded Ms Alexander, the Labour leader, "desperate and inept" as she floundered under a string of blows.
Ms Alexander and her team of advisers had planned to land a killer blow with a surprise revelation that 30 million of cuts were being made at schools across Scotland, thanks to SNP policy.
But the plan began to unravel after the Labour spin doctor Simon Pia inadvertently triggered a chain reaction that tipped off the SNP.
At Holyrood yesterday Ms Alexander began her attack with a challenge about broken promises over education.
Five schools were to be closed in Aberdeen in an 8 million budget cut, while 10 million was being cut from education in Edinburgh, 4 million in Highland, 3 million in Renfrewshire, 2.5 million in Fife, and 1 million in West Dunbartonshire and East Lothian, she said.
"How does the SNP justify 30 million in cuts to education in councils where their party is in power?" she demanded.
She went on to claim the SNP had failed to provide the money for promises made at the election. This included 210 million on reducing class sizes, 30 million for additional support needs, 46 million for sports facilities, access to a teacher for every nursery child, and matching "brick for brick" Labour's programme for 200 new schools.
In response, Nicola Sturgeon, standing in for Alex Salmond, who had been struck down by a stomach bug, cited a battery of recent opinion polls against Ms Alexander, pointing out her unpopularity.
"PhDs in poll ratings and dunces in education," retorted Ms Alexander, before moving on to her intended coup de grce in the final question.
Referring to letters she had received from parents on the parent council of Gleniffer High School in Paisley, Renfrewshire, she raised concerns about the number of Advanced Highers being cut to two.
She claimed that one parent, Fiona Wilkie, feared her daughter would be unable to study a subject she needed for a career in medicine because only two Advanced Higher options would be offered next year instead of five.
Prepared for the question, Sturgeon said Ms Alexander's claim about Gleniffer High was "absolutely untrue" and triumphantly demanded she withdraw the "smear".
"The reality is that Advanced Higher subjects are decided locally on the basis of uptake and individual schools," she said. "That's right for pupils and parents, and right for local accountability."
She went on: "So desperate and inept is Wendy Alexander and the Labour Party and her Labour colleagues that they have had (Ms Alexander's aide] Simon Pia phoning round Renfrewshire this morning trying to stir up this story.
"The headteacher at Gleniffer High School (David Nicholls] was so concerned by their scaremongering that he phoned the (SNP] leader of Renfrewshire Council (Derek Mackay] to complain about Labour's tactics on this issue.
"Wendy Alexander is yet again exposed as coming to this chamber and trying to scaremonger with no facts to back up what she's saying."
Later, a Scottish Government spokesman explained the school currently offers two Advanced Highers and was hoping to add science and art to the curriculum once the appropriate staff had been recruited.
Mr Pia denied that he had been "stirring up trouble".
"I called the school as a matter of courtesy to tell them that they would be mentioned in First Minister's Questions, that was all," he said.
Last night Ms Alexander demanded that Ms Sturgeon retract her comments.
And Ms Wilkie, who is chairwoman of the parent council at Gleniffer High School, defended the Labour leader.
"I specifically raised with Wendy Alexander the withdrawal of Advanced Highers in science and my concerns for my daughter, who hopes to pursue a career in medicine."
MYSTERY OF THE MISSING CONSULTATION PAPER
NICOLA Sturgeon, the Deputy First Minister, was also asked to explain what had happened to a mysterious consultation on student poverty during question time.
Nicol Stephen, the Lib Dem leader, reminded the chamber of an interview First Minister Alex Salmond gave to the BBC when he said that a consultation document had been published on student debt which should soon be available. But, Mr Stephen pointed out, it was not available and when his staff put in a freedom of information request for it they were told: "Releasing information on the policy proposals would not be in the public interest at this time."
Afterwards a Scottish Government spokesman said that the consultation document had been drawn up and will be released in due course.