Havant were left frustrated on their return to action in South Clubs’ Women’s League division one on Saturday.
The Havant College outfit, who are deep in a relegation battle, delivered an encouraging display against Southgate.
But Katie Pugh’s second-half strike was not enough to prevent the London visitors snatching a 2-1 victory.
Havant signed off the first half of the season with a morale-boosting 1-0 triumph over Guildford last month.
Freezing conditions restricted them to just one training session prior to the competition’s resumption on Saturday.
But Drew Emery’s team showed no signs of rustiness as they had the better of the opening exchanges at their Barncroft Way headquarters.
Amanda Hilsdon and Laura Hudson made inroads in the centre of midfield, while Sam Lister picked holes in Southgate’s rearguard down the left flank.
But the hosts failed to make their impressive start pay.
They struggled to deliver the killer pass as a resolute and organised Southgate side defended in numbers.
And they were made to pay with five minutes of the half remaining.
By this point the visitors had grown into the game, putting Havant under pressure and forcing a series of short corners.
And it was one such set-piece that was lashed home via a cruel deflection off the stick of Lauren Thomas-Peter, who was named joint player of the match alongside centre-back Helen Moore.
Moore helped ensure the hosts did not concede again in the first period - before they launched a fightback in the second half. But once again they were frustrated as Southgate continually crowded them out in the final third.
Their bid to get back into the game was further hampered when Dutch forward Eveline Frouws was shown a yellow card and sent to the sin-bin for a wreckless stick tackle.
However, with the odds stacked against them, Havant enjoyed their best period of the game when they were down to 10 players.
Once again the Southgate back line stood strong in the face of heavy pressure, though. And their discipline was rewarded when they sprang a counter-attack and doubled their advantage with a second set-piece.
Southgate’s two-goal cushion lasted less than a minute, though, as Sophie Briggs raced up the other end to win a short corner.
Pugh controlled the injection brilliantly before firing through a crowded D to make it 2-1.
Buoyed by their goal, Havant went hunting for an equaliser. A good interchange between Pugh and Nicola Wright led to Hilsdon lashing the ball dangerously across goal but narrowly out of reach of Hudson at the far post.
Another break from Pugh teed up Wright to find the onrushing Lister with a reverse pass.
But Southgate once again got back in numbers to crowd out the midfielder as she lined up a shot.
While it was a frustrating afternoon for Havant, they retained their four-point cushion over rock-bottom Guildford, who went down 2-0 at the hands of Teddington.