A first half double from James Ward-Prowse and a Dušan Tadić strike secured back-to-back wins for Saints in a 3-0 success over West Bromwich Albion.
The hosts controlled play from start to finish, having got the ball rolling early on through Ward-Prowse’s first effort of the game on five minutes.
The midfielder came back into the side and delivered a perfectly struck free-kick that found the top left corner of the net after Sadio Mané had been fouled.
Ward-Prowse doubled the lead just past the half hour from the penalty spot following a foul on Matt Targett inside the area. Targett himself almost registered a goal before half-time, but Saints led 2-0 at the break
Substitute Dušan Tadić made it 3-0 by finishing off a well-worked team strike in a game that had as many goals as the past five meetings between the two teams combined.
Saints stuck with their new-look formation, but made two changes from the side that started the win over Watford in midweek.
James Ward-Prowse and Victor Wanyama came in for Jordy Clasie and Oriol Romeu, with the latter starting on the bench for the hosts.
And it was a good start from Koeman’s men who moved the ball around well and largely uncontested against a compact and organised Baggies side.
The breakthrough goal arrived with five minutes on the watch after Mané had been brought down just outside the area by Craig Dawson.
The resulting free-kick from Ward-Prowse was hit perfectly as he curled a strike into the top left corner from 25 yards out for a fantastic start to the game.
Visitors Albion were quiet but almost responded in the tenth minute when James McClean’s cross from the left side was met by a smart header from Craig Gardner but the effort flashed wide of Fraser Forster’s left post.
On 22 minutes, Gardner fired over on the half-volley from Stéphane Sessègnon’s cross, but that was as good as it got for the visitors who struggled to control a Saints side that continued to find pockets of space at the other end.
Former Baggie Shane Long was fouled by Gareth McAuley before a 28th minute corner from Ward-Prowse caused trouble for the visitors with Boaz Myhill dropping it, before Albion eventually scrambled the ball clear.
Saints were handed an opportunity to double their lead in the 34th minute when Craig Dawson hauled down the marauding Matt Targett inside the area for a penalty.
Ward-Prowse stepped up to put the ball into the bottom left corner, sending Myhill the wrong way for 2-0.
Two minutes later, it was nearly 3-0 when Targett reacted to Mané’s blocked attempt to see a close range shot cleared from the line by McClean at the far post.
So it stayed 2-0 at the break, with Saints looking comfortable in the contest.
West Brom made a double substitution at the start of the second half with Chris Brunt and Salomón Rondón introduced as part of a reshuffle for the visitors who appeared to line up with a 3-4-3 formation.
The move certainly gave the visitors more impetus in attack, but their first chance of the half was wasted when it came in the 50th minute as Rondón knocked the ball down for Sessègnon who fired over from the edge of the area.
Sessègnon repeated that effort just before the hour mark, with Albion still unable to seriously test Saints at the back.
The hosts swiftly hit on the break to showed their threat a minute later when Davis found Long with an arching ball forward. Long checked back and released Mané into the area who, with the angle against him, flashed the ball wide across the face of goal.
The Baggies still couldn’t force a shot on target, with Victor Anichebe the latest to fire wide from a good position, while Saido Berahino was brought on to try and spark a reply.
Instead, Saints made it 3-0 with 72 minutes on the clock. It was an easy-on-the-eye move that saw Long flick the ball into the path of Davis who then produced a masterful assist. The Northern Irishman shaped to shoot before placing a clever reverse pass to release Tadić who, from six yards out, placed a finish across Myhill.
That was the knockout blow which Albion never recovered from, with Saints going on to see out their third successive home league win in a convincing manner.
Southampton team (3-5-2): Fraser Forster; Virgil van Dijk, José Fonte (c), Ryan Bertrand; Cédric (Cuco Martina 83), Victor Wanyama, James Ward-Prowse, Steven Davis (Oriol Romeu 72), Matt Targett; Sadio Mané (Dušan Tadić 63), Shane Long. Unused substitutes: Kelvin Davis (GK), Maya Yoshida, Graziano Pellè, Juanmi
Goals: Ward-Prowse (5) & (pen) (35), Tadić (72)
West Brom team (4-5-1): Boaz Myhill; Craig Dawson, Gareth McAuley, Jonny Evans, Jonas Olsson(Salomón Rondón 46); Claudio Yacob, Craig Gardner, Darren Fletcher (c) (Chris Brunt 46), James McClean, Stéphane Sessègnon (Saido Berahino 63); Victor Anichebe. Unused substitutes: Ben Foster (GK), James Chester, Rickie Lambert, Callum McManaman
Referee: Martin Atkinson
Attendance: 29,622 (including 1,518 away)