It was a cagey affair on the south coast, but a win for Iraola's side meant that they have overcome the 40 points mark which means the Cherries have pretty much secured Premier League football for another season.
The match started off flat with both teams struggling to string together any rhythm into the game.
However, the first real chance of the game fell to the home side when Ryan Christie unleashed a powerful shot towards goal but was comfortably blocked by the Crystal Palace defence on 16 minutes.
On 26 minutes, the Eagles created their first opportunity of the game when striker, Jean-Philippe Mateta found space on the edge of the box but his shot was straight into the hands of Bournemouth keeper, Norberto Neto.
Straight after, Phillip Billing did tremendously well to get round his defender on half way but dragged his shot past the post from mid-range on 28 minutes.
On 35 minutes, quick feet by Ryan Christie meant that Joachim Andersen dived in and was the first man into referee, Graham Scott's book.
The best chance of the half for Bournemouth came in the 37th minute, when Adam Smith delivered an accurate cross into the six yard box, which found Phillip Billing but his header was saved brilliantly by goalkeeper, Dean Henderson.
However in stoppage time, Eberechi Eze thought he put Crystal Palace in front but VAR said no since Mateta was offside in the build up.
At half time, Iraola brought on Antoine Semenyo for Alex Scott which proved to be influential.
Crystal Palace started the second half on the front foot, with Eze dancing his way through Bournemouth's box but his pass was cut out and the Cherries survived an early scare on 51 minutes.
Will Hughes was the 2nd man put into the referee's book when he blatenly pulled back Adam Smith and stopped a counter attack on 59 minutes.
In the wet and windy conditions, the game was heading for a goalless draw but on 79 minutes, the deadlock was broken when substitutes Antoine Semenyo and Justin Kluivert combined to give the home side the lead and turned out to be the match winner.
The Ghanian International went on a sensational run to get past his defender and found Justin Kluivert in the box, before the dutchman rifled his shot past Dean Henderson.
On 84 minutes, Bournemouth pushed for a second goal to try and wrap up all three points but Antoine Semenyo's shot was saved brilliantly again by Dean Henderson.
In injury time, Justin Kluivert found space on the edge of the box but his shot was beaten away comfortably by Dean Henderson.
Justin Kluviert's strike was the only goal of the game and turned out to be a pivotal one leaving the Cherries 7 points behind sixth place Manchester United.
Iraola was asked after the game about his side chances of possibly finishing in a European place. Here's what he had to say:
"No. The only thing with 41 points is that you know you are safe and are going to be in the Premier League next season".
"We have smaller goals. It's good to be not so far from teams in the top 10".
That is now four wins in five games for the Cherries and are now only five points off equalling their best ever points tally in the top flight.
Crystal Palace manager, Oliver Glasner was disappointed that his side failed to get anything from the game. He said:
"If you don't score a goal you can't win".
"We had many good situations. You need to shoot. Maybe we have to improve, be more indecisive in offensive positions".
This defeat for the Eagles leaves them without a win in four games and just the one in eight.
Oliver Glasner's side are just eight points clear of the relegation zone.
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Man of the Match
Lloyd Kelly was instrumental at the back for Bournemouth keeping a clean sheet for his side but also very influential at being able to switch the play and create offensive opportunites for his team.