Saliba was shown a yellow card for his foul on Evanilson near the centre circle after receiving a poor pass from Leandro Trossard. However, after a VAR review, referee Robert Jones upgraded the card to a red, leaving Arsenal with 10 men on the field for the third time this season.
Bournemouth were already making life difficult for Mikel Arteta's side, who were without the injured Bukayo Saka, and finally made the breakthrough in the 70th minute when a clever corner routine allowed substitute Ryan Christie to slam home an emphatic finish.
Arsenal substitute Gabriel Martinelli had missed a golden chance to put Arsenal in front moments earlier, shooting too close to Kepa Arrizabalaga after the Bournemouth goalkeeper gifted possession to full debutant Mikel Merino just outside his own box.
And the visitors' evening soon went from bad to worse as Justin Kluivert, another Bournemouth substitute, coolly converted from the penalty spot after David Raya had brought down Evanilson.
TrendingThe defeat, Arsenal's first in a Premier League away game since the turn of the year, means they missed the chance to go top of the table, above leaders Liverpool, who they will face without the suspended Saliba, live on next Sunday.
Bournemouth, meanwhile, celebrate a hard-earned victory, their first against a top-six side under head coach Andoni Iraola, which takes them into the top half of the table.
Saliba is usually an unflappable figure in the heart of Arsenal's defence. He had never previously been sent off in his senior career. But there was more than a hint of panic about his decision to tug down Evanilson following Trossard's unhelpful pass.
It seemed he had got away with it when the yellow card emerged from Jones' pocket, the referee deeming the distance from goal to be too great to award a red. But while the VAR intervention was tough to take for the visiting fans, Saliba offered little complaint.
He knew he had erred and Arsenal, beaten for the first time this season and at risk of slipping four points behind Liverpool and three behind Manchester City, both of whom play on Sunday, now face the prospect of going up against the leaders without their most important defender at the Emirates Stadium next weekend.
Arsenal boss Mikel Arteta in his press conference:
"We are obviously very disappointed with the result and gutted because we have to play again in that context. This time was even more difficult than the previous two we faced this season.
"Playing for 65 or 68 minutes with 10 men at this level is just an impossible task. It's an accident waiting to happen, not to get the points. I cannot fault the team for their effort, their commitment, how intelligent they are to play in the way that we have to do it.
"There is a big moment obviously with 0-0 when we have a big opening, one against one with the 'keeper. We don't manage to score and at the other end we do that. We have to fault ourselves.
"Football is a sport where errors are part of that. Tonight we made two big errors that have cost us the game unfortunately."
On whether Arsenal have any plans to appeal Saliba's red card: "That decision was changed and now the decision is not going to change twice. So, decision made.
"We have to accept it, move on and have that pain that we are feeling at the moment for Tuesday [against Shakhtar Donetsk]."
Arteta rued Martinelli's miss shortly before Bournemouth's opener, describing it as the biggest chance of the game. Former Arsenal striker Theo Walcott said on : "For me, he gives the goalkeeper a very clear idea of which way he's going to go straight away. He opens up his body too soon.
"Of course, it's a great save, but look, this is Arsenal, they want to win the league. It's a massive moment for not just Arsenal, but for Martinelli himself.
"You don't have to overthink it. I think at times Martinelli, when he has a bit more time on the ball, he actually overthinks it instead of actually doing something instinctive.
"And I think that's probably what he's down for at times with his goal scoring record at the moment."
Bournemouth boss Andoni Iraola:
"For us it was an important game after losing the last one against Leicester. We had to recover.
"Today we started very well. There was the red card and from then it was tricky as they are still a threat from set plays, free kicks. But we had the patience and ended the game well."
On the clever corner routine for the opening goal: "The advantage they have at set plays is they are taller than us so we had to find another way to make a difference. Today it worked and it was important."
' Jamie Redknapp:
"I was so impressed with Bournemouth today. They make it so difficult for teams. They earned that right today with the intensity. They made Arsenal feel uncomfortable.
"Almost forget the 10 vs 11, the 11 vs 11, that was when Bournemouth were very good. They forced issues, they forced problems. They deserve their result today.
"Iraola has produced so many good things, the players, the style of football. But you need those blue-chip wins, the ones that make a real statement.
"Not just for the team, but also for yourself. And I love the way the team's playing. They're a joy to watch because you see the energy they play with.
"They run without the ball, they run with the ball. They're just a really good side to watch, with a bit of flair and a bit of stardust, with the likes of Semenyo."