She was sacked by the DHB last year.
The tribunal chairman, David Carden, said the professional conduct committee's case was made out, including that the doctor obtained the medicines intending them for use by herself or someone else other than the patient.
The committee's lawyer, Jonathan Coates, said: "Dr Kleszcz has falsely claimed or misrepresented to other health practitioners that she was [the patient's] care worker and/or case worker. Dr Kleszcz has deliberately misled other health practitioners to obtain various medications, including controlled drugs."
He said the doctor's behaviour posed a risk to the public because of the potential to have deprived the patient of medicines he needed.
Carden said that instead of de-registering Dr Kleszcz, the tribunal might have suspended her from practising for a set time or imposed conditions on her practice had she attended the hearing as that would have allowed an exploration of how her issues could be addressed.
Without that discussion, it was necessary to remove her name from the medical register to protect the public. Any discussion of her issues would now be left to the Medical Council, should she in future apply to resume medical practice in New Zealand.
Carden said the council would be asked to notify medical registration authorities in Australia and elsewhere of her being struck off here and the reasons.
Dr Kleszcz's name does not appear on the medical register in Australia.
The tribunal also ordered she be censured and that she pay $21,000 towards the committee's and tribunal's costs.