Holland defender Ake headed home the 10th-minute opener from a Diego Rico corner, before winger Wilson swept in to double the Cherries' lead 10 minutes before the break.
James Ward-Prowse's penalty early in the second period gave Saints hope of a fightback but England striker Wilson seized on a defensive mistake to kill off the game in stoppage time and end the visitors' 15-game winless streak at their near neighbours.
Friday's victory moves Eddie Howe's men to third place in the Premier League going into the weekend fixtures, level on 10 points with champions Manchester City.
Their margin of success would have been greater had Joshua King not had a 25th-minute strike ruled out for offside by VAR.
Southampton are set to resume their bitter rivalry with Portsmouth on Tuesday evening when the Hampshire clubs clash for the first time since 2012.
Saints fans, whose songs suggested they already had one eye on the Carabao Cup third round tie at Fratton Park, have had to be content with Bournemouth for local opposition in recent seasons.
The Cherries made the 30-mile trip east having lost nine of their previous 15 visits, drawing the other six, including the thrilling 3-3 game in late April which secured Saints' top-flight survival.
Ahead of kick-off there was a minute's applause in memory of former Southampton chairman Leon Crouch, who died earlier this month at the age of 70.
Home supporters began the match by taunting the sold-out away end with chants of 'there's only one south coast derby' – but they were silenced with 10 minutes played.
Cherries left-back Rico produced a delightful inswinging corner from the right and Ake took advantage of dreadful defending to get ahead of marker Oriol Romeu and head home his first goal of the season.
The below-par hosts were given a major let-off 15 minutes later when Bournemouth thought they had doubled their advantage.
Norway forward King emphatically slotted in at the end of a counter-attacking move, only for VAR to rule he had strayed marginally offside from Dominic Solanke's through pass.
The away side looked dangerous every time they advanced and they were not to be denied what proved to be an insurmountable two-goal half-time lead.
King and Philip Billing cleverly carved open Southampton's defence on the left, before the latter pulled the ball back to leave Liverpool loanee Harry Wilson a simple finish into the bottom right corner for his third goal of the season.
On the evidence of the opening 45 minutes, League One Pompey may feel they have little to fear next week.
Saints resumed with more urgency and, after Ward-Prowse was narrowly off target, he halved the deficit from the spot.
Bournemouth then wanted a spot-kick of their own when King went down under a challenge from Cedric Soares. The Portuguese full-back made no contact with the ball but referee Chris Kavanagh was not interested and VAR backed his decision.
The visitors were content to sit back in the second half as their opponents pushed for a leveller.
Sofiane Boufal twice tested Ramsdale from distance, while winger Nathan Redmond, in front of watching England boss Gareth Southgate, was denied a goal on his return from an ankle injury by a block from Jack Stacey.
Hope of an equaliser was finally ended deep in added time when Cherries forward Callum Wilson took advantage of hesitancy from Jan Bednarek and Angus Gunn to slot his fourth goal in three games into an empty net and spark wild celebrations in the away end.