Alfie Mawson opened the scoring on 38 minutes as he headed home from Gylfi Sigurdsson's corner. It deflected off Oriol Romeu on the way in.
Saints then levelled on 57 minutes in a much brighter second-half for the visitors.
Shane Long slammed home from close range from Ryan Bertrand's low ball.
But Saints couldn't hold on and were unpicked on the break with 19 minutes left.
Swansea's new singing Luciano Narsingh burst forward before cutting the ball across to Sigurdsson to bounce the ball from past Fraser Forster.
Daily Echo photographer Chris Moorhouse was at Liberty Stadium, so be sure to check out the pictures above.
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