The initial exchanges were finely poised with both teams attacked-minded, looking for an early breakthrough.
George Boyd's shot from the right channel was comfortably dealt with by Southport keeper Ryan Robinson, while at the other end Mark Jackson's close-range volley was hit straight at Alan Julian, who cleared the ball for a corner.
Chris Lane provided a good high ball from the right wing for Dan Kirkup, but his header went over. Southport piled on the pressure as their organisation and sharpness returned to Haig Avenue.
Indeed, they should have taken the lead just before the quarter hour mark when Alex Smith flicked the ball to Tony Gray, who fed Jackson, only for Julian to charge down the close-range effort and clear to safety.
Stevenage settled well, absorbing the early pressure from the home side. Steve Morison did well to find space, with his free header going wide and moments later again seeing his headed chance deflected wide for a corner.
From the resulting corner, Dwane Lee was allowed space and time to aim, with his header also being palmed away to safety by Robinson.
Southport composed themselves, regained control and sneaked into the lead just before half-time when Gray spotted Mark Boyd sprinting from midfield in acres of space, before placing the ball into the bottom left corner of the net.
Boro's response was immediate, with Mark Stimson's half-time team-talk clearly taking effect, as Jon Nurse whipped in a dangerous ball towards the advancing Morison who glanced the ball beyond Robinson.
Moments later, the visitors took the lead when Boyd ran at the Southport defenc, and played the ball to Jon Nurse, who was steaming in on the right channel, who buried the ball home from just inside the Southport box.
The dominance of Stevenage remained, denying Southport possession, with the hosts' most notable first chance of the second half landing to substitute Joe Fowler, but his low shot was comfortably saved by Julian.
Stevenage were denied a third by the offside flag as Morison buried his shot home. Boyd continue to prove a problem to the Southport defence, whipping in a dangerous ball to Morison who guided the ball just over the bar.
Southport were reduced to ten men with five minutes remaining when Lane received his second yellow card of the evening, leaving his team-mates with an uphill struggle, with Awen Douglas thrown on to see if his height could salvage something for Southport.
John Nutter tried an effort from distance towards the end, with Southport unable to mount a serious challenge on goal, as Stevenage secured a valuable three points.