A goal from Frenchman Oliver Giroud, two minutes from the end, prevented Southampton from winning and another failure for Arsenal, who has not been able to settle their objectives in the Premier League, which completes the sixteenth matchday this weekend.
Arsene Wenger's team, outside the Champions League places, wasted a good opportunity to threaten fourth place Chelsea, who lost to West Ham on Saturday.
Arsenal, who have only earned one point in two games (defeat against Newcastle and draw with Southampton), failed to change their situation at St. Mary's.
Mauricio Pellegrino's team took the lead in the 3rd minute. They managed to hold onto their lead until the end. It was a long pass from Serbian Dusan Tadic that Charlie Austin finished off after exposing the visiting defense.
Arsenal regained control but failed to take advantage of any of their chances. The entry of Oliver Giroud, who replaced his teammate Alexander Lacazette twenty minutes before the end, proved providential. The Frenchman took advantage of a great cross from Chilean Alexis Sánchez to break Southampton's resistance.
Arsenal is fifth, three points behind Chelsea. Southampton, who have not won in their last three matches, are in the middle of the table.