CHESTER'S dreams of a run in the FA Cup were shattered at Haig Avenue.
Declan Week's deflected 25 yard shot in the 32nd minute dumped the Blues out of the fourth qualifying round tie.
Chester made just one change from the side that celebrated a 1-0 home win the previous week against Torquay United.
Kane Richards replaced James Akintunde in the Blues' line of attack.
Chester looked sluggish during the early stages and had to soak up a lot of pressure from their hosts.
Sam Hughes and Ryan Astles were called upon to make a series of defensive headed clearances as the Sandgrounders put pressure on the Blues.
Nathan Ferguson produced the first shot of note, but his long range eighth minute shot was dragged well wide of the right post.
Jamie Allen then forced Liam Roberts into a save and the Blues keeper also had to be alert to gather under pressure from Neil Ashton.
Callum Howe's 22nd minute header from Ashton's free kick was held by Roberts as Southport continued to dictate.
Chester were struggling o string their passes together and carve openings, but Richards and James Alabi combined to pick out Ryan Lloyd in the 24th minute whose left wing delivery was chested down to Norman to collect.
Substitute Jordan Chapell replaced Elliott Durrell seconds later who was struggling with an injury.
Alabi forced Norman to gather under pressure on the half hour mark, but Allen responded a minute later with a 15 yard snapshot that flew over the bar.
Southport then broke the deadlock in the 32nd minute when Declan Weeks' 25 yard shot deflected and wrong-footed Roberts to find the net.
Chester attempted to respond, but Alabi's 35th minute shot deflected off a defender and looped over the bar.
Hughes headed wide of the target from a Chapell corner in the 38th minute as Chester searched to get back on level terms.
Alabi raced clear of the offside trap in the 41st minute but his effort was blocked and cleared.
Andrai Jones responded a minute before the break, but his 15 yard effort flew over the bar.
And Chester created an opportunity in first half stoppage time when Lloyd's cross from the right touchline picked out Richards at the far post, but his downward header was claimed by Norman.
Chester started brightly after the break, but Alabi's flicked header from Mahon's 51st minute left wing cross bounced wide of the right post.
But Southport carved a few chances in response with Ferguson finding Roberts with a low shot.
Chapell came within inches of an equaliser on the hour mark, but his low strike from 20 yards deflected wide of the left post.
Akintunde then replaced Richards as Chester continued to press, but Roberts then had to make a great save to deny Lussey from 25 yards.
Chester continued to press in the 66th minute when Alabi found Akintunde with a pass from the left of the area, but Akintunde's first time shot was saved by Norman.
But the Blues struggled to carve open the Southport rearguard despite five minutes of stoppage time.
SOUTHPORT (4-4-2): Norman, Higgins, Howe, Thompson, Ashton, Weeks (G Jones 78), Lussey, Nolan, Ferguson, (Caton 74), Allen (Cofie 84), A Jones. Subs (not used): Grimes, Gray, White, Crump.
CHESTER (4-4-2): Roberts. Vassell, Astles, Hughes, Hunt (Horwood 82), Lloyd, Mahon, Durrell (Chapell 29), George, Alabi, Richards (Akintunde 60). Subs not used): Killock, Evans, Waters, Joyce.
REFEREE: Wayne Barratt (Worcestershire).
ATTENDANCE: 1,674 (738 from Chester).
See Monday's Leader for full match report and pictures.