Gary O'Neil has been the interim manager of Bournemouth for the last three months.
Dominic Solanke gave the Cherries a lead after just over a minute.
The lead was restored by Jefferson Lerma before the half-time break.
O'Neil has been in charge of four draws and two victories.
Following defeats by West Ham and Newcastle, the Cottagers battled hard to get a point.
The result leaves Bournemouth in ninth place in the league, while Cottagers are one place and a point away from the drop.
After yet another impressive display by the Cherries, O'Neil is giving himself a good chance of being the permanent successor toParker.
With the prospective takeover by Bill Foley yet to be finalized, it seems certain that O'Neil will keep his job.
His confident side took just 64 seconds to get off to a great start when Marcus Tavernier sent Philip Billing and Solanke on their way.
When Solanke set up Lerma, he made no mistake from the edge of the box.
Bournemouth spent most of the second half on the back foot and rarely threatened to get back in the game.
On the back of a six-game winning streak, they should relish the chance to take on their neighbours.
There is more to come.
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