Superb vision from George Boateng midway through the first half gave Hull a chance to take the lead as the ex-Boro man hit a 30-yard ball up to Geovanni in space, but the Brazilian's square the ball across the six-yard box was well cut out by David Wheater.
Geovanni was then found in space by King as the Wigan loanee picked him out with a curling left-footed cross, but Hull's leading scorer got his header all wrong as he sent the ball well wide of the target.
The home side were awarded a free-kick on the half-hour mark as Jeremie Aliadiere brought down Geovanni on the edge of the box, the ex-Barcelona man took it himself but his right-footed effort was deflected wide of the post.
Stewart Downing had a chance for the visitors just before the break as an Aliadiere cross from the right found its way to the England international, but his left-footed strike from just inside the box whistled just past the post.
Geovanni stepped up a gear in the second half and nearly created the opener as the Hull man skipped past two defenders and played a ball into King, but the Tigers frontman could only smash his shot well wide of the post from close range.
It was Middlesbrough who took the lead on 79 minutes as Justin Hoyte raced down the right and played in a low cross towards Tuncay, who cleverly backheeled the ball past Boaz Myhill and into the net from close range.
However Hull were back on level terms a minute later as substitute Bernard Mendy picked the ball up on the right-hand side of the box and fired in a low shot which saw the ball hit the post, bounce off back off keeper Ross Turnbull and roll over the line.
Phil Brown's men were then awarded a penalty on 85 minutes after Wheater saw red for bringing down Geovanni in the area.
King took the spot-kick and buried the ball underneath the outstretched Turnbull and into the bottom corner of the net to make it 2-1.