The visitors took the lead as Connor Woods beat his man and his cross was converted by Jordan Archer. Into the second half, it was Woods who doubled their advantage, catching Atkinson off his line from 30 yards.
It was the home side that dominated the early stages and could’ve taken an early advantage.
After good work from Nicky Clee and Adam Nowakowski, a loose ball was struck first time by midfielder Isaac Marriott from 20 yards which deflected wide.
After a penalty shout from the Avenue dugout for an alleged foul on Jake Hibbs, which was waved away by the referee, Nowakowski had two decent chances to break the deadlock.
A lovely cross from Harry Boyes was met by the number nine and, leaning back, Nowakowski nodded over from eight yards.
Shortly after, a back-pass to goalkeeper Daniel Hanford saw the No.1 make a mistake and Nowakowski was alert to the rebound, but Hanford recovered to make a save.
As the half went on, Liam Watson’s side were having success down their right wing with Woods and Matt Challoner striking up a good partnership and they were rewarded for their efforts.
Woods got behind his marker near the touchline and fizzed a low ball into the box. Archer got in front of his man to tap home from close range.
Into added time, the Avenue nearly equalised as Clee weaved his way through a gap, staying on his feet after an earlier challenge, but his delivery was flicked over by Hibbs from 14 yards.
After the break, a similar pattern of play continued as the visitors seemed content to allow Bradford have possession in their own half, as long, diagonal balls were failing to stick up front.
It was Southport FC who scored the next, vital, goal to seal victory. A long throw from Lewis Knight was nodded away and Woods was set free near the touchline. The winger spotted Atkinson off his line, and after the goalkeeper slipped on the surface, the ball looped over him and into the the net from 30 yards.
Despite making substitutions, Mark Bower’s side were finding it difficult to break down a stubborn and disciplined opponent. Despite a second yellow card for Matt Challoner, Southport FC restricted the Avenue, who didn’t trouble Hanford and in the end, eased to a victory in West Yorkshire.
Bradford (Park Avenue): Atkinson, Ross, Boyes, Marriott, Lund (Downing 84), Havern (c), Toulson (Sanyang 66), Hibbs, Nowakowski, Knight, Clee (Windass 78)
Subs not used: Huffer, L.Lyons
Yellow cards: Lund, Nowakowski, Marriott
Southport FC: Hanford, Oliver, Doyle, Benjamin ( Anson, Ali 72), Morgan, Woods (Vassallo 84), Challoner, Archer (Carver 79) Watson, Bainbridge.
Subs not used: McMillan, Winnard, Vassallo.
Goal: Archer (26), Woods (68)
Yellow cards: Challoner x2, Ali
Referee: Paul Cooper