Arsene Wenger's Gunners created a number of scoring chances throughout but were unable to get past Fraser Forster and his defence in what was a massive slip-up from the North London club.
Arsenal had lost 4-0 to Ronald Koeman's Saints on Boxing Day and were desperate to exact revenge on the south coast outfit but could not breach Forster who was making just his fourth appearance after spending 10 months on the sidelines with a knee injury.
Forster did brilliantly to keep out Mesut Ozil early when denying the German after he took a sublime touch and shot before again keeping out the Gunners playmaker from close range.
The Saints keeper then acrobatically denied Olivier Giroud's curling right-footed effort in the opening minutes of the second half before glancing wide a header from Alexis Sanchez.
It was just never going to happen for Arsenal who produced 10 shots on target but in the end, dropped points and fell to fourth on the table with Leicester City, Manchester City and Tottenham all winning their fixtures.
Arsenal are now five points off the league-leading Foxes and just five points ahead of fifth-placed Manchester United while the Saints, who have kept four clean sheets on the bounce, edged ahead of Liverpool into 7th.
2015/16 BARCLAYS PREMIER LEAGUE - SEASON SCORES
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