Alexis Sanchez's 88th minute goal stole the points for Arsenal at the Emirates as ten-man Southampton could not hold on.
In a game which neither side looked overly dominant, it was an injury to Southampton's Toby Alderweireld that was the deciding factor. Having already lost Jack Cork and Dusan Tadic to injury on the night, Alderweireld tweaked a hamstring and limped off, leaving the Saints to play out the remaining ten minutes with ten men.
That allowed the home side to pile on the pressure, which told late on as the Saints could not clear and Sanchez was left unmarked to tap home the winner from six yards out.
Comfortable opening period
Southampton manager Ronald Koeman opted for Cork and Shane Long to replace Morgan Schneiderlin and Sadio Mane for the trip to the Emirates Stadium, hoping for his side's second win their this season.
A bright opening for the visitors saw Graziano Pelle spurn the best opportunity as his one-two with Steven Davis saw the Italian striker blaze over from the corner of the six-yard box.
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The only downside of the half was the injury to midfielder Cork, who went off with the recurrence of a recent ankle injury after a hefty tackle.
Injuries stacking up
Tadic was also replaced in the second half due to a knock on his ribs, although the wide man was largely ineffectual throughout and would probably have made way regardless.
Arsenal opened the game up and Fraser Forster saved well from Danny Welbeck before the defining moment of the match. With the Saints having made all three subs, Belgian international Alderweireld tweaked his hamstring and had to limp off, leaving them with ten men for the remaining period.
Unable to hold on
With the man advantage the home side pushed forward in search of a winner, although Forster was doing everything in his power to stop Arsenal from scoring with a heroic performance.
His long arms clawed back an Olivier Giroud header which seemed destined for the net before the home side finally broke down the England goalkeeper's resistance.
After Aaron Ramsey had tip-toed his way to the byline, his pull back found an unmarked Sanchez who tapped home to break the Saints resolve and steal all three points for Arsene Wenger's men.
Defeat was harsh on Koeman's side, who would have fancied themselves for a point with 11 men on the field, but their display will give them hope ahead of their next fixture against Manchester United on Monday night.
Southampton player ratings
Forster - 9
Clyne - 7
Fonte - 7
Alderweireld - 8
Bertrand - 7
Wanyama - 8
Cork - 6
Davis - 7
Tadic - 5
Long - 6
Pelle - 6
Yoshida - 6
Mane - 6
Mayuka - NA