In contrast to Southport, North Ferriby United, who came down from the National League with them at the end of last season, are finding things extremely tough and suffered a humiliating 5-0 home defeat by Brackley.
The carnage didn`t begin until the 35th minute when central defender Luke Graham headed home the opener following a corner.
It was only 1-0 at half-time, and then on 72 minutes Jimmy Armson made it 2-0 from the penalty spot after he had been brought down in the box.
That opened the floodgates and just 3 minutes later, Armson made it 3-0 when he was sent through on goal.
And Armson completed his hat-trick on 84 minutes after good work from Matt Lowe.
Armson`s amazing day continued when he scored his fourth and Brackley`s fifth after 86 minutes.
Darlington were only a goal short of matching the Saints as they beat Alfreton Town 4-1 at Blackwell Meadows.
Alfreton took the lead inside the opening minute when Craig Westcarr saw goalkeeper Adam Bartlett block his effort, but Chris Sharp was on hand to net from close range.
But just a minute later James Caton levelled matters with his first goal for the Quakers.
The hosts took the lead for the first time on 37 minutes when Dave Syers’ header was blocked and Josh Gillies fired home the rebound.
Eleven minutes into the second half, David Ferguson beat Chris Elliott from Caton’s pass to make it 3-1.
And Ferguson was involved in the fourth goal which was Gillies` second of the game on 63 minutes.
Southport made it three wins from three games after beating newly-promoted Leamington 1-0 at the New Windmill Ground.
The only goal of the game came 15 minutes from time from substitute Ethan Jones, who slid the ball home from a tight angle past `keeper Tony Breeden following a short back-pass.
Like North Ferriby, FC United of Manchester are still searching for their first points of the new season after losing 2-1 at home against Kidderminster Harriers, foe whom this was a first three-point haul.
The home side had the lead inside 7 minutes, Danny Wisdom turning the ball home at a corner.
But on 20 minutes, Manny Sonupe headed in a Dan Bradley cross to level things up.
The second half was almost all Harriers and after several near misses, Sonupe finally gave Harriers the lead with 10 minutes to go.
Relegated York City made it two wins from three games with a romping 5-0 win at Bradford Park Avenue`s Horsfall Stadium.
Daniel Parslow gave them a 3rd minute lead that was soon added to by Amari Morgan-Smith's double on 12 and 25 minutes and skipper Sean Newton adding a fourth on 32 minutes.
The Minstermen finally added a fifth 20 minutes from time with Luca Havern heading Louis Almond's cross into his own net.
But York finished the game with ten-men after Hamza Bencherif was sent-off for pulling back former Minsterman Adam Boyes.
Gainsborough Trinity recorded their first win of the season at Nuneaton Town.
There was little action in the opening exchanges until the visitors took a 13th minute lead when a corner from Craig King was swept home from close range by Michael Jacklin.
Boro had the majority of the game but Trinity defended for their lives to prevent an equaliser.
Newly-promoted Blyth Spartans were another side to get off the dreaded nil-points mark with a 4-2 win over Tamworth at Croft Park.
The visitors opened the scoring thanks to a fantastic goal from Reece Styche on 14 minutes, before Ryan Hutchinson scored Spartans’ first goal of the season 4 minutes later.
Strikes from Daniel Maguire and Jarrett Rivers either side of half-time put the home side ahead, but Styche’s spot-kick halved Tamworth’s deficit on the hour-mark.
Blyth were awarded a penalty of their own on 66 minutes, which allowed Dale Hopson to score his first goal for the club and wrap up Blyth’s first three points of the new season.
AFC Telford United were handed their second straight defeat as they were beaten 2-0 by Salford City at the New Bucks Head.
Jake Beesley after 10 minutes and former Bucks striker Mike Phenix on 77 minutes struck in each half for the Ammies, who were watched on by former Manchester United and England full-back, and co-owner, Gary Neville.
Harrogate Town were held to a point at Edgeley Park to drop their first points of the campaign.
Two goals in the space of 5 minutes midway through the first half from Simon Ainge, including a memorable volleyed opener, put Harrogate firmly in command at the interval.
But in front of 3,107, County came back strongly in the second half and Jason Oswell struck back 8 minutes after the restart with a clever near post finish,
And 18 minutes from time Oswell pounced to turn Sam Minihan's shot into an empty net.
It`s won one, lost one and drawn one now for both Chorley and Curzon Ashton as they shared the points at Victory Park.
Curzon snatched the opening goal after 9 minutes when a mistake by Andy Teague allowed Joe Guest to go through and slot past Matt Urwin from a tight angle.
The home equalised on 27 minutes as Teague made amends for his earlier error when he crossed for Scott Leather to find the back of the net.