While it was joy for the Cherries, it was a truly miserable afternoon for Hull boss Mike Phelan, who was taking charge of the Tigers for the first time since being made permanent head coach earlier this week.
Bournemouth made the perfect start on five minutes when Stanislas' free-kick hit the post and Charlie Daniels was on hand to volley home the rebound from around the penalty spot.
Stanislas then nearly doubled the Cherries' advantage but his shot from Jordon Ibe’s low cross struck the crossbar.
Hull had offered precious little as an attacking force at that stage but were gifted an equaliser on 34 minutes.
Steve Cook gave the ball away cheaply to Robert Snodgrass, who fed Ryan Mason, and his shot deflected off Cook and past a wrong-footed Artur Boruc.
Cook didn’t have to wait long to atone for his error. Just seven minutes later he met Stanislas’ free-kick to head beyond David Marshall and put Bournemouth back in front.
Seconds before the break Bournemouth won a penalty when Stanislas was fouled by Snodgrass in the area. Stanislas took the spot-kick himself and slammed the ball home.
The second half proved to be one-way traffic as Bournemouth seemingly cut through the Hull defence at will.
Stanislas got his second and Bournemouth’s fourth when he converted Adam Smith’s cut-back from the right touchline.
It was five soon afterwards when substitute Josh King crossed from the right and Callum Wilson, who was completely unmarked, had the simple task of nodding the ball home past an exposed Marshall.
The win was wrapped up in fine style late on when substitute Dan Gosling ran on to Charlie Daniels’ pass and curled home a wonderful first-time effort into the corner.