It was another good performance from Jamie Milligan's men against higher opposition despite the scoreline, their second game against a side from the National League North in four days.
They started brightly, Wisdom making a surging run forward before placing his effort agonisingly wide.
Danny Roccia then made an excellent diving save to parry behind Dylan Vassello's drive, before Callum King-Harmes forced a similar save from Dan Hanford in the Southport goal with a header.
Brig opened the scoring on 41 minutes, a ricochet in the Southport defence falling into the path of Wisdom who calmly slotted the ball beyond Hanford and into the bottom left corner.
Carver then equalised for Southport on the stroke of half time, heading the ball beyond Roccia.
Brig introduced Richie Allen into the action for the second half, and he got involved immediately by heading the ball into the path of Wisdom in the box, only for Southport to scramble the ball clear.
The visitors took the lead on 49 minutes, the trialist tapping in at the far post from a driven cross.
Allen then fired an effort into the side netting as Brig continued to push, before Hanford got in the way of the Brig number 18's drive.
Southport scored their third goal on 83 minutes, the trialist running through and finishing into the bottom left corner.
3-1 was the way it ended in what was an even match, and another good workout for Brig as the season comes closer into focus.