First half goals from Steven Davis and Graziano Pelle were enough to clinch all three points for the hosts, who lost Victor Wanyama to a second bookable offence in the closing stages.
Southampton came close early on in this encounter as Pelle snuck in behind the Cherries defence, but Simon Francis was able to deflect the striker’s attempt over and out for a corner.
Moments later Sadio Mane found space on the edge of the penalty area and released a strike, but this time Sylvain Distin was on hand to deflect away the danger.
Mane and Pelle then linked up for Saints as the Italian nodded down for Mane to strike, but his effort into the ground bounced safely over the crossbar.
Southampton then took the lead on the half-an-hour mark. A swift passing move down the left found Davis waiting at the back post and the 30-year-old then tucked the ball away from close range.
The lead was then to be doubled five minutes later. Tadic sent in a cross from the same left flank and Pelle was able to rise the highest in the penalty area before nodding past Federici.
Despite the 2-0 score line, the Cherries almost had one back before the break. As an on-rushing Dan Gosling headed Glenn Murray’s initial deflected shot just wide of the post.
Eddie Howe then changed the side up at half time with a double substitution, as Junior Stanislas and Joshua King replaced Marc Pugh and Glenn Murray.
The substitutions soon made an impact on the game, as the Cherries began the second half with renewed vigour.
Substitute Stanislas came closest with a 25-yard free kick after Harry Arter was felled by Virgil Van Dijk, but the 25-year-old’s effort fell just wide of the Southampton post.
Fellow substitute Lee Tomlin then made an immediate impact on the game as he drove at the Southampton defence and was chopped down by Wanyama.
Referee Craig Pawson not only awarded a free-kick for the challenge, but also issued the Kenyan with his second yellow card and subsequent marching orders.
Despite a lively display from substitute Tomlin in the closing stages, Eddie Howe’s men were unable to capitalise on the man advantage and Southampton held out to secure all three points.
Cherries: Federici, Smith, Francis, Distin, Daniels, Surman, Arter (Tomlin, 72), Gosling, Pugh (Stanislas, 45), Ritchie, Murray (King, 45)
Not used: Allsop, Cargill, MacDonald, Kermorgant