MPs unanimously supported the second reading of the Stalking Protection Bill, which would enable police to issue stalking protection orders.
Rotherham MP Sarah Champion said the orders, which give powers to ban strangers from contacting an individual or their families, could be the 'difference between life and death'.
Currently if an offender is a victim's partner, or former partner, police can use domestic violence protection orders to try to curb their behaviour.
The new orders would be applicable to all types of stalking, but would address a gap in the law surrounding offences where strangers are involved.
Welcoming the Bill, Ms Champion said: "In too many cases there isn't enough evidence for police to make an arrest before it's too late.
"The stalking protection orders put forward in this Bill will be an important early intervention tool available to police officers whilst a criminal investigation is ongoing.
"An early intervention could literally be the difference life and death."
Home Office minister Victoria Atkins said the Bill would provide police with a 'vital additional tool with which to protect victims of stalking and deter perpetrators at the earliest opportunity'.
She said: "The order will put the onus on the police not the victims to bring these orders."
The Bill also received support from Labour and will now progress to the committee stage, where it will receive line by line scrutiny.