Nathan Ake's 10th-minute header and Harry Wilson's sweeping finish in the 35th gave Bournemouth a 2-0 lead by halftime, with the visitors also having a penalty decision overturned by the video assistant referee because of an offside against Josh King.
Southampton improved after halftime and pulled a goal back through James Ward-Prowse's 53rd-minute penalty, awarded after Che Adams was brought down by Steve Cook. Bournemouth resisted late pressure from Southampton before Wilson clinched the win in the fifth minute of injury time, with his fourth goal in three games.
Bournemouth moved onto 10 points, the same number as second-place Manchester City. "It is way too early but obviously it's great to be here," Ake said of Bournemouth's current position in the top four.
It was the first game in the sixth round of the Premier League. Bournemouth had previously drawn six and lost nine of the 15 games played away against Southampton in all competitions.
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