Krystian Bielik's first-half strike proved the difference as the Rams moved out of the relegation places.
The Cherries lost further ground on the top two, dropping to fourth after Reading's win over Coventry, having won just one of their last six league games.
Derby started with plenty of intent and Kamil Jozwiak almost gave the hosts an early lead.
The Pole beat his marker at the back-post but saw his goalbound header turned behind by alert Bournemouth goalkeeper Asmir Begovic.
The visitors then wasted a glorious chance when a simple diagonal punt found Jack Stacey on the right flank and his whipped cross just evaded the lurking Dominic Solanke.
A lengthy stoppage then followed after a head injury to Bielik and that affected the flow of the game upon the eventual restart.
Derby's troubles in front of goal have been evident this season and they were perfectly encapsulated on the half-hour mark.
Lee Buchanan suddenly found himself bearing down on goal inside the box but his effort was too tame and allowed Begovic to smother it to safety.
But the hosts' frustration was short-lived as just a minute later they were toasting an opener – and it was the beleaguered Bielik who got it.
The groggy midfielder rose highest from a corner and saw his header partially blocked, before reacting quickest and stabbing home.
Bournemouth made two changes at the interval in a bid to get back into the game and one of them, Josh King, came close to an immediate leveller only to plant a header straight at home keeper Kelle Roos.
The game was starting to open up with Solanke firing a half-volley into the side netting before Nathan Byrne failed to get enough power behind his shot down the other end.
Derby could have doubled their lead just after the hour mark when Matt Clarke met a corner with a stooping header but the feet of Begovic kept the defender's effort out.
Bournemouth upped the ante heading into the final quarter of the game and Wilshere's arrival came with 13 minutes to go.
It was the former Arsenal and England man's first appearance of any kind since a League Cup tie for West Ham last September.
The visitors pushed and probed, with Solanke seeing a header well kept out by Roos, but a resolute Derby held out for a precious victory.