Saints take a 1-0 lead into the semi-final second leg at Anfield in two weeks' time.
Saints could have had a few goals, but will bepleased to have the lead at the half-way stage.
It was Nathan Redmond, with his fourth goal of the season, who gave Saints the advantage on 20 minutes.
The England Under-21 international linked onto Jay Rodriguez's wonderful flick to slot home past Loris Karius.
Liverpool owned much of the pressure, but, even with Philippe Coutinho entering the fray with half an hour to go, weren't able to make it pay.
Photographer Stuart Martin was at St Mary's Stadium, so be sure to check out the pictures above.
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