Turner forced Kamil Zayatte to put through his own net in the 76th minute, but £10million striker Darren Bent had already done the bulk of the damage. He converted a 13th-minute penalty and then made it 3-1 with 66 minutes gone after Andy Reid's 49th-minute strike.
The Tigers had briefly got themselves back into the game with Zayatte's 43rd-minute equaliser, but they were ultimately well beaten.
It took the hosts just 13 minutes to get their noses in front, and they did so with a helping hand from the visitors. Craig Fagan handled Reid's ball into the area and Bent duly obliged from the spot.
Sunderland rarely looked to be in any trouble, but endured an uncomfortable conclusion to the first half with Zayatte heading straight at Craig Gordon from Stephen Hunt's free-kick, and then looping another effort over the bar from an Ibrahima Sonko long throw.
Worse was to come with two minutes of the half remaining. Gordon flapped at Geovanni's free-kick and, from the resulting corner, Zayatte headed Kamel Ghilas' cross home to level.
The hosts forced their way back in front within four minutes of the restart, Reid dispatching a left-footed effort past the keeper with venom.
The game was effectively over with 66 minutes gone as Hull once again contributed to their own downfall.
Anton Ferdinand's ball over the top found Bent in acres of space and, as the blue shirts inexplicably backed away from him, the striker ran in on goal to beat the stranded Boaz Myhill from point-blank range.
The agony increased for the visitors when Turner forced Zayatte to put through his own net with 14 minutes remaining.