A dramatic final 15 minutes saw Chelsea boss Sonia Bompastor sent off after Sjoeke Nusken had given the Blues late hope of a Women's Champions League quarter-final second-leg comeback against Arsenal, but the Gunners were 3-2 winners on aggregate.
Nusken's goal was arguably deserved for Chelsea as they won 1-0 on the night but they were unable to overturn the 3-1 deficit from the first leg as they were left to rue a string of missed chances.
The spark came around the 80th minute when Stina Blackstenius headed home, thinking she had sealed Arsenal's semi-final place, but VAR ruled the goal out for offside.
Chelsea immediately went up the other end, but Nusken missed the opportunity, having also done so twice in the opening eight minutes.
The Germany international also forced a spectacular save from Daphne van Domselaar in a chaotic quarter of an hour, with the Gunners stopper also keeping out a Lauren James rocket. Veerle Buurman sent the rebound onto the post, after she was denied a goal by VAR in the first leg last week.
In the fourth of five added minutes at the end of the second half, Nusken fired Chelsea ahead, but the biggest drama was yet to come.
Bompastor had been tetchy with the officials for most of the game, following on from her criticism of VAR to disallow Buurman's goal for a supposed foul on Laia Codina at the Emirates.
But she was incandescent when Katie McCabe was not penalised for pulling the hair of Alyssa Thompson. Rather than the Arsenal player receiving a yellow card, it was Bompastor who went into the referee's book.
Less than a minute later, the Chelsea coach tried to pick up the ball quickly from the feet of an Arsenal player and in the melee, encroached on the pitch. That was another yellow and then a red, as she watched the final moments through the plexiglass along the side of the Stamford Bridge tunnel.
It was overall a frustrating night for the Blues, who will feel they had more than enough chances to win the game. Thompson, Nusken and Sam Kerr all went close, but it was too little, too late as they exit the Champions League - the one trophy they are yet to win - for another year.
For Arsenal, though, they reach the semi-finals once again as their title defence continues, and will face either Lyon or Wolfsburg, who play their second leg on Thursday evening.
Bompastor was left furious by the decision not to send McCabe off, saying it was a "clear" red card.
"The disappointment is huge," she said of Chelsea's Champions League exit. "We wanted to come into this game and give our all.
"In terms of performance we did what we had to do, we created a lot of opportunities but we didn't score. That is the reality. That is why we are not qualified for the semi-finals.
"But a lot of emotions because I think at the end of the game, some decisions were really controversial."
On the hair pull, she added: "For me, it is clearly a red card for the Arsenal player. She's pulling Alyssa Thompson's hair. If the VAR is not able to check that situation, I don't know why we have the VAR.
"She doesn't have a red card - it is clearly a red card - and, yeah, I go on my emotions. I shouldn't but, at the end, I'm the one with the red card.
"If you look at all the decisions in the first leg and second leg, that's part of the result at the end. That's really disappointing."
"No, I don't want to speak to them because it's always the same story," Bompastor said when asked if she had spoken to the officials.
"Even if I go and speak to them, they will not give me a clear answer. It's difficult for me because I don't want to be the only one talking about this situation.
"But everyone needs to understand that's the difference between being qualified and not being qualified. It has a big impact on players.
"I'm really proud of my players, I think they gave everything and they don't deserve that level of refereeing again."
Chelsea defender Lucy Bronze to BBC Sport: "There's not much more we could do across both legs. We were the better team but not the most clinical. That was the difference.
"They had clinical finishes in the first game which gave us an uphill battle against a top team. We knew we could get the win tonight which is obviously what we did but too many missed chances and crossbars.
"We could be proud of what we did. There's not much more we could do... We need to take that energy and focus into the end of the season because there's still things to play for."
On how far away Chelsea are from a Champions League title: "Not far. The competition has tightened up and the first leg killed us a bit. We went toe to toe with Arsenal who are the current champions and we beat them tonight and should have had better result in the first leg.
"It depends on each game and who turns up. Last year, every one had Barca as the favourites but Arsenal went on the day and clinched it. That's the Champions League, you have to show up and be counted and score the goals."
Meanwhile, Arsenal boss Renee Slegers was delighted with her side's mentality as they kept their hopes of winning a second straight Champions League title alive.
"It was a very hard scenario going into this game with a two-goal lead," Slegers said. "The three games before this game had been very tight with small margins.
"We were preparing for this again. So proud of the players, mostly from a mentality perspective - how they managed this game. Really proud of the mentality again."
On McCabe's hair pull on Thompson, she added: "I have seen the still picture back. I didn't see the incident on the pitch when it was happening but I did see Katie going to Alyssa to apologise. My assumption is it's not intentional but it is of course unlucky. I have to watch it back before I comment more."
Arsenal captain Kim Little to BBC Sport: "We haven't had the start to the season that we wanted but we have grown as the season has gone and been really dominant in competitions.
"Ultimately that's not good enough. You want to be consistent and league champions. We need to make sure we are consistent and on it. We discuss that about how we have better starts.
"It would be nice to do it two years in a row, we'll give it all we can."
