The Cherries bossed the match from start to finish, hitting the woodwork and having several penalty shouts turned away, but Leicester rode their luck to come away with a point.
Eddie Howe's side came flying out of the blocks and could have been a couple of goals to the good inside the opening five minutes.
Defoe had another chance moments later when he raced onto a skilful through-pass from Lewis Cook, only for Wes Morgan to make a good recovery tackle. Marc Pugh still might have put Bournemouth ahead when he ran onto the loose ball and dragged wide from the edge of the box.
When another rebound fell to Pugh on 43 minutes, the winger, who has scored twice previously against the Foxes - in the Premier League and Championship, scuffed wide on his weaker left foot.
The best of Bournemouth's spot-kick appeals came when Harry Maguire clumsily tangled with King on the right edge of the box. Danny Simpson also survived a couple of instances of possible handball when referee Graham Scott erred on the side of caution on each occasion.
Jamie Vardy started for Leicester despite being omitted from the England squad this week because of a hip injury, but he was starved of service on an afternoon when Craig Shakespeare dropped Riyad Mahrez for Bournemouth's summer transfer target Demarai Gray.
Gray was one of two Leicester players who came close to snatching them an undeserved win in the second half when he cut inside from the left and hit a sweet, dipping strike which Asmir Begovic had to tip over the crossbar.
Those were the only two moments that Leicester had while Bournemouth laid siege to their goal for the opening 70 minutes, before running out of steam.
They tested Kasper Schmeichel when Junior Stanislas shot low from Adam Smith's pass, and Andrew Surman may have had the Danish stopper beaten when he met King's layoff which dropped just over the crossbar.
It was only an end product that was missing from Bournemouth's performance, and a lack of goals will be a concern for Howe now that his side have found the net only four times in their opening seven league games.
The Cherries break for the international fixtures in the bottom three, with Leicester only spared the same situation by goal difference.