Story of the match
The hosts dominated possession in the early exchanges, but were unable to carve through a resolute Luton Town defence.
And, it was The Cherries who had the first opportunity of the game, when Josh King latched onto Luke Berry's loose header, but the Norwegian international was unable to make enough contact to lift the ball over the on-rushing Simon Sluga in the Town net.
Both sides struggled to create chances from then on in, and the visitors started to see more of the ball with Harry Cornick particularly causing problems for The Cherries defence.
In the 26th minute, Bournemouth were reduced to ten men, when Jefferson Lerma received his marching orders for catching Tom Lockyer in the face when the pair contested for a header.
Lockyer tried to continue after the collision, but eventually made way for Luton's new signing Kal Naismith, who only joined The Hatters 24 hours ago.
Despite being a man down, Bournemouth picked up the tempo and once again looked the better side. In the 36th minute, King was once again denied by Sluga, firing into the arms of the Croatian goalkeeper from a rather tight angle.
The Hatters failed to record a single shot in the first half, so whatever Nathan Jones said at half-time had a clear impact on his Luton side with Luton forcing Asmir Begovic into a succession of saves early in the second 45.
The first of which fell to centre-back Glen Rea who saw his effort kept out by a combination of Begovic and Solanke.
The resulting corner saw the former Chelsea keeper deny Berry's volleyed effort, before acrobatically keeping Kiernan Dewsbury-Hall out with his follow up.
James Collins concluded a five-minute spell of madness with a header from Harry Cornick's cross that narrowly sailed wide of the far post.
Bournemouth responded well to Luton's early pressure and started to dominate the ball once again. Solanke thought he had opened the scoring in the 54th minute when he slotted past Sluga from King's perfectly weighted through ball, but the forward was denied by centre-back Dan Potts.
Dewsbury-Hall fired the visitors into the lead in the 67th minute, with on-loan Leicester City man curling an effort beyond Begovic after brilliant play from Cornick on the right wing.
Bournemouth continued to pile the pressure on The Hatters, with Rodrigo Riquelme's volleyed effort stinging the palms of Sluga after a well-worked move down the right.
Despite Bournemouth initially reacted well to the red card, it eventually changed the course of the game and allowed The Hatters to start the second half a lot brighter than they would have. Bournemouth still enjoyed a lot of possession, but with fewer runners going in behind, they found it difficult carve through the Luton defence.
It means that The Cherries have only won a single game in their last five and have lost even more ground on the automatic spots. A disappointing result for Bournemouth, who will be eager to put things right midweek.
For the hosts, David Brooks was a threat all afternoon. He started on the right wing and put some inviting crosses into the area. After Lerma’s sending off, he took up a more central position and still had the same impact from a deeper role.
Kiernan Dewsbury-Hall ultimately scored the decisive goal and performed brilliantly for The Hatters. He was a constant threat going forward and kept possession very well in tight areas. The on-loan Leicester midfielder also worked very hard from a defensive perspective winning crucial heads and making vital tackles.