The hosts, who were knocked out of the FA Cup by League One side Rochdale on Saturday, fell behind in the 14th minute when winger Ben McKenna made a penetrating run down the right flank and produced a neat finish.
Barrow, having been watched by a crowd of 4,414 at Holker Street for the cup tie, were looking to improve on sixth place in the National League table, and went close to an equaliser before half-time when an acrobatic effort by defender Moussa Diarra hit the crossbar.
Southport could have extended their lead in the second half, but Andrai Jones' close-range effort was saved by Jonathan Flatt as the visitors held out to secure a crucial three points in their battle to pull clear of the relegation fight.
Report supplied by the Press Association.
Match ends, Barrow 0, Southport 1.
Second Half ends, Barrow 0, Southport 1.
Substitution, Southport. Jake Wright replaces Delial Brewster.
Substitution, Barrow. Lindon Meikle replaces Jordan Williams.
Substitution, Barrow. Ross Hannah replaces Richard Bennett.
Substitution, Barrow. Andy Haworth replaces Dan Rowe.
Second Half begins Barrow 0, Southport 1.
Jordan Williams (Barrow) is shown the yellow card for a bad foul.
First Half ends, Barrow 0, Southport 1.
Goal!  Barrow 0, Southport 1. Ben McKenna (Southport).
First Half begins.
Lineups are announced and players are warming up.

The Manbij Military Council, part of the Kurdish-led Syrian Democratic Forces (SDF) alliance, announced it had "transferred defence of the frontline".
The move came after a deal was agreed with Russia, a staunch ally of President Bashar al-Assad, it added.
The villages have been a focus of fighting in recent days.
There was no immediate comment from the Syrian government or Turkey, whose troops have been supporting a rebel offensive aimed at driving Islamic State militants from a border area north-west of Manbij and limiting gains by Kurdish fighters.
Syria's military has accused Turkey of a "flagrant violation of Syrian sovereignty".
Since launching Operation Euphrates Shield in August, the Turkish-backed rebels have captured more than 1,900 sq km (734 sq miles), according to Turkey's state-run Anadolu Agency.
After they captured the IS stronghold of al-Bab last month, Turkish President Recep Tayyip Erdogan declared that the rebels would next move towards Manbij.
Mr Erdogan also said the Kurdish Popular Protection Units (YPG) militia, which dominates the SDF and the Turkish government considers an extension of the banned Kurdistan Workers Party (PKK), should be forced to withdraw.
The YPG captured Manbij from IS militants in August, but it agreed three months later to move its forces east of the River Euphrates after setting up the Manbij Military Council with local Arabs.
But Mr Erdogan rejected claims by the US that Kurdish fighters had left.
On Wednesday, a spokesman for the Manbij Military Council told Reuters news agency that a string of eight villages about 27km (17 miles) west of Manbij that it controlled had come under heavy artillery bombardment by the Turkish-backed rebels and that there had been fierce clashes.
One SDF fighter and two Turkish-backed rebels were killed in the fighting, according to the UK-based Syrian Observatory for Human Rights.
On Thursday, the Manbij Military Council said in a statement that defending the town and countering Turkey's "invasion plan" were among its objectives.
It had therefore "agreed with Russia to hand over villages on the frontline with Euphrates Shield... to the border guards of the Syrian state", the statement added.
Syrian government forces are deployed just to the south of al-Bab and were involved in clashes with the Turkish-backed rebels shortly before the town fell.
In a separate development, the commander of the US-led coalition against IS said Russian aircraft had mistakenly bombed SDF fighters 16km (10 miles) south-west of Manbij, resulting in an unspecified number of casualties.
Lt Gen Stephen Townsend said the Russian military had thought it was bombing villages held by IS.
However, Russian media cited the Russian defence ministry as denying that Russian or Syrian aircraft had launched any strikes on US-backed forces.
Barrow suffered a narrow home defeat by Southport on their return to National League action.
[NEXT_CONCEPT]
A US-allied Syrian militia has said it will hand over villages west of the town of Manbij to the army in order to stop Turkish-backed rebels taking them.