There were four changes from the side that lost 2-0 to Tottenham Hotspur in a defeat lacking in fight and character last weekend, with Maarten Stekelenburg, Cuco Martina, James Ward-Prowse and Shane Long all coming into the starting line-up.
Three of the four goals came courtesy of the fresh faces, with Martina getting proceedings underway in truly spectacular fashion after just 19 minutes.
After a soft header away by Per Mertesacker, Martina rushed on to the ball before thumping a bending strike past Petr Cech from 30 yards with the outside of his right boot.
The goal lit the match to set the atmosphere insight St. Mary's alight, as Saints grew in confidence.
Long should have made it 2-0 before the end of the first half, but after racing in on goal he poked hopelessly high and over Cech's goal.
Saints got in with the score still 1-0 at the break, before taking the game to the Gunners in the second half.
The advantage was doubled after Long stroked home from close range after 55 minutes. After linking up with Steven Davis, the Irish forward combined with Sadio Mané, with the Senegalese forward putting the ball on a silver platter for Long to convert.
14 minutes later, it was 3-0. Ryan Bertrand's whipped corner to the near post was met at speed by the head of José Fonte, with the Saints skipper notching his 15th goal for the club after escaping the attention of Alex Oxlade-Chamberlain.
Dušan Tadić forced a save from Cech with a rasping drive from distance after emerging from the bench, before Long saw a low effort bounce clear off of the foot of the far post.
Long struck again in the 90th minute, wrapping up a sublime and much-needed victory for Saints by outpacing Mertesacker and firing the ball through Cech's legs to complete the scoring.
Arsenal struggled to create opportunities, and when they did they rarely tested Stekelenburg, with Mesut Özil watching a late effort bobble across the face of goal before being cleared by Bertrand.
Victory saw Saints close the gap on European qualification to five points, with a trip to West Ham United scheduled for Monday.
Southampton: Stekelenburg; Martina, Fonte, Van Dijk, Bertrand; Wanyama; Ward-Prowse (Tadić - 71'), Clasie (Romeu - 67'); S. Davis; Long, Mané (Juanmi - 81').