They said the “surprise” findings, reported at the European Breast Cancer Conference, could mean some women no longer need chemotherapy.
The drugs, tested on 257 women, target a specific weakness found in one-in-ten breast cancers.
Experts said the findings were a “stepping stone” to tailored cancer care.
The doctors leading the trial had not expected or even intended to achieve such striking results.
They were investigating how drugs changed cancers in the short window between a tumour being diagnosed and the operation to remove it.
But by the time surgeons came to operate, there was no sign of cancer in some patients.
Prof Judith Bliss, from the Institute of Cancer Research in London, said the impact was “dramatic”.
She told the BBC News website: “We were particularly surprised by these findings as this was a short-term trial.
“It became apparent some had a complete response. It’s absolutely intriguing, it is so fast.”
Image copyrightSPLThe drugs were lapatinib and trastuzumab, which is more widely known as Herceptin.
They both target HER2 – a protein that fuels the growth of some women’s breast cancers.
Herceptin works on the surface of cancerous cells while lapatinib is able to penetrate inside the cell to disable HER2.
The study, which also took place at NHS hospitals in Manchester, gave the treatment to women with tumours measuring between 1 and 3cm.
In less than two weeks of treatment, the cancer disappeared entirely in 11% of cases, and in a further 17% they were smaller than 5mm.
Current therapy for HER2 positive breast cancers is surgery, followed by chemotherapy and Herceptin.
But Prof Bliss believes the findings could eventually mean some women do not need chemotherapy.
However, that will require larger studies especially as HER2 positive cancers have a higher risk of coming back.
“We would have to be very clear we’re not taking a backwards step and increasing the risk of relapse,” Prof Bliss added.
Baroness Delyth Morgan, the chief executive at Breast Cancer Now, said: “We hope this particularly impressive combination trial will serve as a stepping stone to an era of more personalised treatment for HER2 positive breast cancer.
“Such a rapid response to treatment could soon give doctors the unprecedented ability to identify women responding so well that they would not need gruelling chemotherapy.”
Breast cancer is now thought of as at least ten separate diseases, each with a different cause, life expectancy and needing a different treatment.
Matching the specific errors in a tumour to targeted drugs is considered the future of cancer medicine.
Breast cancers, and particularly HER2 positive tumours, are at the forefront of this revolution in treatment.
Prof Arnie Purushotham, from Cancer Research UK which funded the study, said: “These results are very promising if they stand up in the long run, and could be the starting step of finding a new way to treat HER2 positive breast cancers.”
