Nathan Ake put the Cherries ahead after six minutes with a fine header, but Ryan Bertrand's equaliser moments later shifted the momentum completely. The Saints were dominant thereafter, particularly after the break, and Jay Rodriguez's double meant Claude Puel's side left the Vitality Stadium with all the spoils.
The result means Southampton pull away from Eddie Howe's team and move up to seventh.
Hosts hit the ground running
After a cagey opening few minutes with both sides getting glimpses of an opportunity, it was Bournemouth who took the lead. A short corner was cleverly worked into the path Jack Wilshere, and his teasing in-swinging delivery from the right picked out a diving Nathan Ake at the far post, whose powerful header beat Saints keeper Fraser Forster, with the ball nestling in his bottom right-hand corner.
The breaking of the deadlock marked a brief period of Cherries dominance, a miscommunication between Virgil Van Dijk and Sofiane Boufal allowed Josh King a clear sight of goal, but his ferocious left-footed strike was just about kept out by Forster.
Saints strike back
Then, out of nothing, Southampton were level. Left-back Ryan Bertrand cut inside his opposite number Adam Smith with ease, before unleashing a low, fizzing shot across Artur Boruc and into the far corner, meaning that the Saints were, perhaps undeservedly, on level terms again. As it happened, it was the turning point of the game.
Just as Bournemouth should have perhaps netted twice in quick succession with King's chance, Puel's men arguably could have been ahead minutes after equalising. Good pressure from Nathan Redmond and Jay Rodriguez allowed Boufal to let fly from the edge of the penalty area, but his deflected shot fell kindly for Boruc.
The best chances continued to fall to the away side, with Bertrand finding Redmond with a low cross from the by-line. However, as has been the case so often this season for Southampton the opportunity went begging, as the forward couldn't make any meaningful contact.
Yet as the first-half continued, the goalmouth action dried up, meaning that the South Coast rivals went into the break all square.
One-sided second half
Claude Puel has been criticised by many around St Mary's in recent weeks for his tactical decisions, but whatever he said in his half-time teamtalk was very effective, as they came out of the tunnel looking far the better side. Redmond pounced on a weak header from Simon Francis, but Ake did just enough to prevent him from getting a decent shot away.
However, that only delayed the inevitable. Substitute Steven Davis made an almost immediate impact after coming on for Harrison Reed at the break. The Northern Ireland captain linked up intricately with Boufal, before delicately lifting the ball over Boruc, and Jay Rodriguez was there to tap home, ending his three month goal-drought by putting the Saints in front.
Southampton kept the tempo high and had plenty of possession, but were unable to increase their lead. A Rodriguez shot from a narrow angle was saved by Boruc and a low drive from Pierre-Emile Hojbjerg was cleared off the line by Ake. As a result, the sides entered the final quarter of the game with all still to play for.
Despite Bournemouth pushing forward in ever-increasing numbers, it was the away side who kept coming the nearest to troubling the scoreboard. With ten minutes to go, Redmond came close again, his curling effort from long-range was just too high to trouble Boruc.
Rodriguez seals it in style
And then, with little over five minutes remaining, the points were secured for Southampton spectacularly. With the ball bouncing around just outside the area, Rodriguez netted his second with an astonishing and unstoppable shot on the turn which dipped just enough to find the top corner.
The relief and ecstasy was clear to see in the celebrations of the Saints players, staff and fans, as they go three points ahead of their neighbours with just their second away win of the season.