On a frustrating night for home supporters, the Mariners failed to fire against visitors who had lost their previous four games without scoring a goal.
Brodie threatened to put the visitors ahead before half-time, before the returning Lenell John-Lewis missed two chances for Town either side of the interval.
In a game of few chances, Town created the better opportunities but they were hit with a sucker punch eight minutes from time, when Brodie struck to settle the game in Southport’s favour.
John-Lewis replaced Rhys Oates in attack as Town boss Paul Hurst made just one change to the starting XI after Saturday’s win against Chester.
Otherwise, it was as you were, with James McKeown in goal behind a defence of Danny Parslow, Toto Nsiala, Shaun Pearson and Carl Magnay.
The midfielders were Jack Mackreth, Craig Clay, Scott Brown and Scott Neilson, with John-Lewis partnered by Ross Hannah up front.
The Grimsby subs were Oates, Paul Bignot, Craig Disley, Paul Walker and Patrick McLaughlin.
Nsiala and Brown were both lining up against their previous club for the first time since moving east in the summer.
And two familiar names to home fans were included in the Southport side in the shape of ex-Town players Clayton McDonald and Brodie.
Grimsby were looking to make it three wins out of three, while their visitors were hoping to stop a poor run of defeats and claim their first away victory in 28 attempts.
An early Southport free kick was dealt with by Nsiala before a shot from midfielder Stephen Brogan cleared the Pontoon Stand from 25 yards.
A foul by Nsiala brought another free kick on seven minutes but Brogan’s left-footed shot hit the Grimsby wall.
After a quiet opening to the game, Grimsby’s first attack of note saw Hannah look for John-Lewis but the ball was cut out for a throw-in, before an effort from Parslow on the right was blocked.
Town were beginning to see more of the ball and for longer periods after the 10-minute mark but were yet to create any danger in the final third.
Parslow had to head clear at the far post after a dangerous cross from the Southport right as the visitors mounted a short spell of pressure on 17 minutes, although the ball eventually finished with McKeown.
The visitors appeared to be gaining in confidence but a promising Grimsby move came when Neilson chipped the ball into the box for John-Lewis, although the striker could not control it.
Soon afterwards, Brodie found some space after turning past Pearson on the edge of the Town box but he could only shoot across McKeown’s goal.
Brodie won a free kick on the right on 24 minutes but Paul Smith’s far-post delivery was headed away from danger by Pearson.
Clay and Hannah then combined a minute later to create a shooting chance for the striker, although his low 20-yard effort lacked the power to beat visiting keeper David Raya.
Brown was the next to let fly for the Mariners, smashing a low shot wide of the mark after being teed up by Hannah on the edge of the box.
A foul by Dominic Collins on John-Lewis gave Town a free kick to the right of the penalty area but Hannah wasted the opportunity, chipping the ball wide of the far post.
Clay hit a shot over the bar from 25 yards as the hosts continued to look for an opening goal, although Raya was still untroubled in the Southport goal.
Hannah won a corner just after the half-hour and Brown looked for the head of Pearson from the flag but McDonald got to the ball first and headed it clear.
Brogan was shown the first yellow card of the game for a foul near the halfway line and Nsiala’s ball from the resulting free kick was headed away by McDonald as far as Parslow, whose shot was blocked.
A chance for the visitors came when a cross from Matt Challinor found midfielder Scott Kay but his weak shot bobbled through to McKeown.
Brown was booked after a foul six minutes before the break and the away side had the ball in the Town box again soon afterwards, when a driven cross from David Fitzptrick on the left had to be headed away by Pearson.
Neilson sent a dipping shot over the bar from 25 yards as Southport got men back and made things difficult for the home attack.
McKeown was called into action when Brogan found Brodie on the edge of the Town box but the keeper was alert to the danger and raced off his line to make the block.
The Mariners could have taken the lead as the game moved into one added minute but John-Lewis could only fire at keeper Raya from 10 yards.
John-Lewis then headed over the bar after a cross from the right and that proved to be the last opportunity of a frustrating first half for the Mariners and their supporters.
Goalmouth action had been at a premium at both ends, with neither side able to force a breakthrough.
No changes were made before the restart and the first chance for Town to get the ball into the danger zone came after a foul on John-Lewis four minutes in. Neilson’s delivery from the right was a good one but the referee spotted an infringement inside the box and signalled for a Southport free kick.
Brogan pushed a shot wide of McKeown’s goal from 20 yards on 56 minutes, with the game still yet to really come to life as a spectacle.
A header from John-Lewis proved comfortable for Raya at one end, before Brodie and Parslow both slipped near the Town box but the visitors were unable to create a chance.
Perhaps the best opportunity of the game so far came on the hour when Hannah’s pass sent John-Lewis through on goal but after advancing into the box, he dragged his shot wide.
Neilson, Kay and Brodie were all shown yellow cards after an incident near the Findus Stand touchline inside the Town half.
Pearson joined them in the referee’s notebook after bringing down Brogan, who had set off on a run through the middle on 68 minutes. Smith hit the free kick over the bar from 25 yards.
Hannah tried a snap-shot from a similar distance at the other end soon afterwards but could only watch it bounce through to keeper Raya.
Another yellow card was produced for Southport’s Challinor after he brought Neilson down with 18 minutes to go.
Town manager Hurst chose that moment to make a double substitution, sending Disley and Oates on for Clay and John-Lewis.
The move seemed to give the hosts a boost, as they forced a corner and had a short spell of pressure which suggested they could be about to step up a gear.
Southport also fired a warning that they were still looking for maximum points when Brogan set Fitzpatrick up on the edge of the box but McKeown got down well to tip his shot away.
A cross from Magnay at the other end was headed behind for a corner by McDonald and from the flag, the Mariners almost had their breakthrough when a towering header by Nsiala was cleared off the line.
Brodie won a corner off Parslow on 82 minutes and from the flag, the visitors forced their way ahead when Smith’s cross was not cleared and BRODIE pounced to fire home as the Town defenders appealed for offside.
Town now had eight minutes to save the game and Brown tested Raya with a stinging drive from 30 yards, although the keeper was equal to it.
John Marsden replaced Brodie with four minutes to go, while McLaughlin came on in place of Parslow for Grimsby.
Brogan cleared the bar with a shot from 20 yards as Southport looked to make the points safe.
Magnay hit a shot wide as the game moved into stoppage time and a free kick 30 yards out gave them one last chance to salvage something from the game but Hannah sent his shot over the bar.
That meant it was disappointment for Town and their fans, leaving the small band of travelling Southport supporters to celebrate a rare away success.
The Mariners will aim for better things when they travel to Dartford on Saturday.