Southampton 2 Arsenal 0: Koeman's side strengthen grip on fourth
Sadio Mane and Dusan Tadic both accepted gifts from the visitors' defence at St Mary's Stadium to give Southampton a seventh home win of the season.
Mane opened the scoring after 34 minutes with a sublime goal from a tight angle, the in-form 22-year-old lifting the ball over stranded Arsenal keeper Wojciech Szczesny.
Fraser Forster kept his side in the game with three quality saves to deny Santi Cazorla and Alexis Sanchez, before Arsenal handed the hosts a second.
Tadic profited as Arsenal failed to clear a cross inside their six-yard box, the Serb firing home from close range to seal the points shortly before the hour.
It could have been worse for Arsene Wenger's side had Mathieu Debuchy not headed off the line to deny Graziano Pelle, but it mattered little as Southampton moved three points clear of their opponents in the standings.
A bright start from the hosts should have been rewarded with a goal in the seventh minute as Tadic escaped the attentions of Per Mertesacker on the left.
He lifted a perfect cross on to the head of Pelle, but the striker's header was kept out by the foot of the post.
Arsenal welcomed back midfielder Tomas Rosicky as one of three changes, and the Czech was involved in creating a chance for Cazorla after 20 minutes.
The 34-year-old raced onto Sanchez's throughball on the right, and his pull back found the Spaniard inside the penalty area but Forster was on hand to keep the visitors at bay.
But the deadlock was broken by Southampton in the 26th minute when Mane produced a moment of genius to beat Szczesny.
The Senegal international latched onto a James Ward-Prowse's pass behind the Arsenal defence, and reacted to being pushed wide by Szczesny by curling an audacious chip over the Polish keeper and into the unguarded net, despite Mertesacker’s best efforts.
Ward-Prowse - one of three changes for the hosts - should have doubled Southampton's advantage before the break with a low shot that Szczesny saved easily, and Ronald Koeman was then forced into a change when Mane limped off with a hamstring injury.
The visitors started the second half with renewed attacking threat, and Sanchez went close to levelling 10 minutes after the break only for Forster to produce an excellent low save.
And - as in the first half - Koeman's team immediately punished them for failing to take their chances as Tadic took advantage of more slack Arsenal defending.
Mathieu Debuchy and Szczesny failed to clear Steven Davis' right-wing cross, and the loose ball fell to Tadic, who made no mistake from six yards.
Arsenal should have been further behind after 65 minutes when a woeful back pass from Laurent Koscielny was intercepted by Tadic.
He found Pelle, but Debuchy atoned for his previous mistake with a headed clearance off the line.
Sanchez fired a free-kick just over Forster's bar late on, but Southampton deserved their victory.