Environment Minister Mark H Durkan said the Road Traffic Bill would "save lives on our roads".
The drink-drive limit in Northern Ireland would be reduced by almost 40%.
Under the plans, the permitted blood alcohol limit would be reduced to 50mg of alcohol in 100ml of blood - down from the current UK limit of 80mg.
It would be the first major shake up in Northern Ireland's drink drive laws since the limit was introduced in 1968.
The bill also includes restrictions on new young drivers carrying passengers immediately after they pass their test.
The assembly gave its backing to new drivers up to the age of 24 not being allowed to carry more than one young passenger (aged 14 to 20, except immediate family members) during the six months after they pass their test, between the hours of 10pm and 6am.
The minister, Mr Durkan, said: "This is an important milestone towards reducing deaths on our roads.
"I welcome assembly backing for the lower drink drive limits, for a new graduated driver licensing scheme, and a new requirement for quad drivers to wear a helmet when riding on roads.
"There is also compelling evidence of the heightened risk of collisions when new young drivers carry teenage passengers.
"Young drivers carrying two young passengers are twice as likely to be killed as driving alone, and four times more likely to die if carrying three young passengers.
"The assembly has given its backing for young people not carrying passengers during night-time hours, for the first six months after they pass their test. I would like to see this being for the full 24 hours and feel there is still work to be done to the legislation regarding that."
The bill will now go to further consideration stage.
A bill that would see lower legal alcohol limits for drivers has passed through another stage at the Northern Ireland Assembly.