Burnley gave another impressive away day showing as they came away from St Mary's with all three points in a game that lacked quality throughout.
Chances were few and far between, but a Sam Vokes header was enough for Sean Dyche to leave the south coast the happier of the two managers.
There was little to choose between the two sides in the early proceedings. Southampton saw more possession without threatening, while Burnley looked comfortable soaking up pressure, hoping to hit the Saints on the counter attack.
Both teams were guilty of lacking that final moment of quality to give their sides a chance of opening the scoring. Crosses were continually over-hit, while play in the final third would break down all too often at St Mary's Stadium.
The first real chance came midway through the first half, as a Sofiane Boufal half-volley from a Redmond cross was smartly saved by Nick Pope in the Burnley goal as the noise around St Mary's began to rise.
It was now Southampton in the ascendancy as they looked more likely to score the opening goal of the game. Ryan Bertrand had two efforts in the space of five minutes, his second was much more threatening, but was blocked well by the impressive James Tarkowski to keep the scores level.
Burnley offered very little as an attacking threat in the first half and were soon under pressure again. Redmond attacked at pace, cut inside and unleashed a fierce low drive that Pope was equal to and pushed behind for a corner in what was the final notable action of a rather uneventful half.
Both Mauricio Pellegrino and Sean Dyche would be expecting more in the second half in a game that had up until this point lacked any real quality.
The second half started in much the same way as the first, with a failed corner routine from Southampton summing up the game.
That soon changed as Pope failed to deal with a Saints corner, which fell to Maya Yoshida who turned and shot with a dipping volley. Pope was able to redeem himself and tip the effort over as Southampton looked to up the tempo of the sluggish affair.
Burnley now looked to attack for the first time with any real purpose, as substitute Sam Vokes was played in by Robbie Brady, but his cut-back failed to find a claret shirt and the Saints could clear.
With the game appearing to be heading for a draw, Burnley took the lead in the last ten minutes of the game.
Johann Gudmundsson cut back onto his left to deliver an in-swinging cross that Vokes beat Yoshida to, and directed his header to Fraser Forster's bottom left corner from their first effort on target to give Sean Dyche's side a timely lead.
Southampton plugged away for an equaliser without having the quality to do so, as Burnley looked comfortable seeing the game through with Dyche's men giving another impressive showing on the road.
Lee Probert sounded for full-time that brought an end to a forgettable encounter at St Mary's that seemed destined to end goalless, until Sam Vokes' late header secured all three points for the visitors.