It looked for a long time like Palace wouldn't pick up their first point of the Premier League season, as they stayed behind for most of the game following Josh King's early goal, but Dann was in the right place at the right time to convert from Jason Puncheon's 93rd minute cross.
The big team news was Alan Pardew handing a full debut to new summer signing Christian Benteke, with the Selhurst Park faithful giving him a huge welcome, keen to see what he could offer them.
King with an early goal
Unforunately for the Eagles, it was at the other end of the pitch where much of the game was spent early on, with Bournemouth taking the lead after just 10 minutes.
Josh King was the goalscorer, taking the ball from Harry Arter in some space on the edge of the area, before beating Steve Mandanda with a right-footed shot into the bottom corner.
Cabaye misses penalty as Cherries enjoy solid first half
Palace did respond to that, winning a penalty soon after, giving them an excellent chance to level up. Mike Dean, who was criticised last weekend for giving two penalties for slight offences, was at it again, pointing to the spot after Charlie Daniels had a little tug of Benteke's jumper.
Although he's known to be prolific from the penalty spot, Benteke didn't step up, Yohan Cabaye allowed to continue from the spot this season, something that Pardew lived to regret as the Frenchman had his effort kept out by Artur Boruc. Cabaye's day got even worse a minute later, as Dean booked him for a late challenge in the middle of the pitch.
Bournemouth took confidence from the penalty save, pushing forward as King - lively throughout the first half - had a shot blocked before Andrew Surman drilled an effort over the bar.
Palace did have the odd chance as the half went on, Joel Ward forcing Boruc back into action with a left-footed strike, but it was the Cherries that were still in control, Callum Wilson attempting to tease Mandanda with a chipped effort, one that the new 'keeper was equal to.
Pardew's team talk works wonders as Palace push on
Alan Pardew was clearly not a happy man at half-time, and whatever he said must have worked, Palace improving hugely in the second 45.
Bournemouth, troubled straight away, dropped deeper and deeper as the game went on, with 'keeper Boruc booked for dissent as he became frustrated with his defence's disorganisation.
The chances were slowly coming for Palace, Benteke heading just over from a cross, whilst Andros Townsend had an effort saved after doing what he does best, cutting inside to take a shot.
Palace were shooting from everywhere, Chung-Yong Lee and Pape Souare both going for goal, but nothing was working for the Eagles. When Benteke thought he'd been brought down in the area by Adam Smith, only to see his appeals waved away, you'd have been forgiven for thinking that it wasn't to be their day.
However, Pardew's side weren't giving in just yet, continuing to pour forward as the game entered stoppage time, and the pressure eventually paid off.
Dann destructive at the death to square the score
Scott Dann was well up the pitch, determined to net an equaliser for his side, and did so. Puncheon crossed, finding the centre-back, who powered a bullet header past Boruc and into the back of the net, sending Selhurst Park wild.
There was little time for more play after that, leaving Eddie Howe agonising as Bournemouth's first three points of the season turned into one, and Alan Pardew delighted as Palace surprisingly picked up their first of the campaign. Still, there's work to be done for each team as the league pauses for the first international break of 2016-17.