Members of the Scottish Medicines Consortium (SMC) heard that the therapy, called Kadcyla, had enabled patients dying from the disease to lead "almost normal lives".
Experts advised the meeting it was more effective and less toxic than other available treatments and there was an "unmet need" to help the women targeted - those whose cancer has spread and who have tried other treatments.
However, SMC members raised questions about the cost and efficacy of Kadcyla.
Ian Crichton, of the SMC, asked for the views of clinical colleagues, adding: "It is extremely expensive, which is a choice on the part of the company, and while they give a discount ... it is not exactly a generous one, so we do end up with something that is a very high price but of questionable ... effectiveness."
The drug has already caused furore in England, where the National Institute for Health and Care Excellence (Nice) has so far rejected it for routine use on the NHS and criticised manufacturers Roche for not setting an affordable price. Sir Andrew Dillon, chief executive of Nice, said it "could not recommend Kadcyla at the price it proposed".
While trials show it can extend life by six months, it is said to cost £90,000 per patient. Documents before the SMC yesterday described a course of treatment as costing £55,471. The paperwork predicted 118 patients would be eligible for treatment a year when Kadcyla was first introduced, rising to 177 within five years. Assuming some savings were made because other prescriptions would be replaced by Kadcyla, the cost to the Scottish NHS was estimated at £1.82 million, rising to £4.98 million within five years.
During the meeting one SMC member noted the number of oncologists who could be hired for the same money.
The drug has come before the SMC at a crucial time. Following a review by the Scottish Government, new systems have been launched to improve access to the latest drugs including the creation of a Patient and Clinician Engagement (PACE) group that is meant to give both a stronger voice in SMC decision-making.
SMC meetings were also opened to the public for the first time in May and Kadcyla is the most controversial drug the members have considered since then.
Alison Campbell told the SMC meeting in Glasgow that the PACE group that discussed Kadcyla expressed strong support for the treatment. The results experienced by clinicians who had used the drug were "perhaps even better" than those reported by official trials, she said.
"This medicine gave women a normality to their life and this contrasted sharply with what would be expected with a diagnosis of metastatic breast cancer," she explained.
Afterwards James Jopling, director for Breakthrough Breast Cancer in Scotland, described the drug as "an amazing advance".
He said: "One of the clinicians was quoted as saying if there is one drug the SMC was to support, it should choose this drug.
"At this stage in this new process I don't think I could hope for more than that in terms of compelling evidence being presented for why patients and doctors want to see Kadcyla approved. What is very difficult to say is how that is going to be taken account of in the decision-making process.
"We're going to have to wait and see how SMC members weigh up the undoubted strong and passionate case from those who have witnessed this drug and taken this drug versus the fact we know this is a very expensive treatment and one that has already been rejected by the NHS in England.
"It is an incredibly difficult decision but our position is that this is a ground-breaking new treatment for breast cancer for women who don't have any other options."
Members of the SMC voted on whether to accept Kadcyla via a secret ballot at the end of the meeting, but the results of this are not announced immediately.
The decision is expected to be announced on October 13.