The Assisted Dying for Terminally Ill Adults (Scotland) Bill, brought forward by Scottish Liberal Democrat politician Liam McArthur, passed the stage one vote by 70 votes to 56.
Under the bill only those who have lived in Scotland for at least 12 months, and who are registered with a GP in Scotland, would be able to make such a request.
There would also be a period of at least two weeks between a request being made and the necessary medication being provided, with the patient having to be able to take this themselves.
It had originally been planned that people could apply for an assisted death from the age of 16, but an amendment to 18 is on the cards.
The stage one vote was on the general principles of the bill, it will now face further votes at the committee stage and in the chamber before potentially becoming law, but not until early next year.
The assisted dying bill relating to England and Wales is due to go before MPs in the House of Commons on Friday (16 May) for its report stage, where various further amendments will be debated and voted on.