Curtis Bateson's second goal of the season got the visitors off to a dream start after eight minutes.
The 21-year-old took the ball around goalkeeper Magnus Norman and slotted home shortly after Ryan Fallowfield struck a post as the visitors seized early control.
Rory McKeown levelled things up six minutes into the second half by tapping in Ben McKenna's low cross, before North Ferriby took complete control.
Connor Oliver put the visitors back in front with a spectacular strike from 25 yards in the 69th minute.
Ryan Kendall made it 3-1 with five minutes remaining and Reece Thompson added further gloss to the scoreline in the 89th minute.
Declan Weeks netted a consolation for the hosts in stoppage time, but the game was long over.
Report supplied by the Press Association
Match ends, Southport 2, North Ferriby United 4.
Second Half ends, Southport 2, North Ferriby United 4.
Goal!  Southport 2, North Ferriby United 4. Declan Weeks (Southport).
Goal!  Southport 1, North Ferriby United 4. Reece Thompson (North Ferriby United).
Ryan Kendall (North Ferriby United) is shown the yellow card.
Goal!  Southport 1, North Ferriby United 3. Ryan Kendall (North Ferriby United).
Substitution, Southport. Declan Weeks replaces Rory McKeown.
Jake Wright (Southport) is shown the yellow card.
Substitution, North Ferriby United. Ryan Kendall replaces Danny Emerton.
Goal!  Southport 1, North Ferriby United 2. Connor Oliver (North Ferriby United).
Goal!  Southport 1, North Ferriby United 1. Rory McKeown (Southport).
Second Half begins Southport 0, North Ferriby United 1.
Substitution, North Ferriby United. Sam Cosgrove replaces Matthew Templeton.
First Half ends, Southport 0, North Ferriby United 1.
Substitution, North Ferriby United. Ross Armstrong replaces Ryan Fallowfield.
Goal!  Southport 0, North Ferriby United 1. Curtis Bateson (North Ferriby United).
First Half begins.
Lineups are announced and players are warming up.

The singer sought damages from the force, and the BBC, over media coverage of a police raid on his home in 2014.
On Friday, lawyers told High Court judge Mr Justice Mann that Sir Cliff and the force had come to terms.
The BBC, which is still disputing the claim for damages, said it "had a duty to report" the investigation.
Sir Cliff said live BBC coverage of the police search of his home in Sunningdale, Berkshire, invaded his privacy.
He sought "very substantial" compensation from both South Yorkshire Police and the BBC.
In a statement on Friday, a BBC spokesman said: "The BBC's responsibility is to report news stories that are in the public interest."
The corporation said the "extensive disclosure of historical child sexual abuse" by other celebrities made the investigation - and a subsequent police decision to search his home - a worthy news story.
"A search happened, and because it did, the BBC reported it - just as any other media organisation would have and did," the spokesman said.
South Yorkshire Police had already apologised "wholeheartedly for the additional anxiety caused".
The force learned of the sex offence allegations in July 2014, searching Sir Cliff's Berkshire flat the following month.
In June 2016, the Crown Prosecution Service announced Sir Cliff would face no charges.
The star's lawyers said he suffered "profound and long-lasting" damage from coverage of the search, and from being publicly named as a suspected sex offender.
They also say South Yorkshire Police contravened guidance on "relationships with the media".
Second-bottom North Ferriby crushed Southport at the Merseyrail Community Stadium.
[NEXT_CONCEPT]
Sir Cliff Richard and South Yorkshire Police have settled a legal fight over reports naming him as a suspected sex offender.