Eighty-six MSPs voted for the Alcohol Bill, none opposed it and 32 Labour MSPs abstained.
The price per unit is expected to be announced next month and brought into force early next year.
Health Secretary Nicola Sturgeon admitted minimum pricing was not a “magic bullet that will solve all of our nation’s problems with alcohol”.
But she said: "It is essential if we are to make a significant contribution to reducing consumption. The link between price and consumption, and consumption and harm, is irrefutable.”
Labour MSPs have criticised the policy, saying it will not affect drinking among young people and may bring retailers a windfall.
Labour's Richard Simpson, a former GP, said he accepted that minimum pricing would have “some effect on some of the very serious harmful drinkers”, but warned that poor people would be hardest hit by the move.
“The less well-off, who are drinking safely and moderately, will have to pay a price for those who are drinking irresponsibly," he said.
The next step for the Alcohol Bill is the committee stage in April, when MSPs will scrutinise the bill to iron out problems and Sturgeon is expected to announce the price per unit.
If it then passes a final vote in June, it will get royal assent in October and pass into law. Retailers will have just a few short months to prepare before the law comes into force in early 2013.