A late header from Axel Disasi rescued a 2-2 draw for Chelsea at Brentford, but supporters turned against Blues manager Mauricio Pochettino.
Chelsea looked to put their Carabao Cup final defeat further behind them having beaten Leeds in the FA Cup on Wednesday, and they were on course to do so when Nicolas Jackson deservedly headed them in front during the first half.
Brentford had been hanging on for half-time but were transformed after the break, with Mads Roerslev pouncing in the box to equalise within five minutes of the restart before Wissa's brilliant acrobatic volley put them ahead.
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Chelsea supporters began chanting against co-owner Todd Boehly, singing the name of Jose Mourinho and calling for Pochettino to go as Brentford looked to put the game to bed with Sergio Reguilon's header hitting a post.
But Disasi had the final say, nodding home at a corner in the 83rd minute after Bees goalkeeper Mark Flekken had cheaply conceded the set-piece. Chelsea remain 11th in the Premier League while Brentford are six points above the relegation zone.
How Chelsea denied Brentford
Brentford matched Chelsea during the opening 25 minutes but faded badly once the visitors got hold of possession. Pochettino had changed the Chelsea formation to three at the back for the first time in 21 games to help deal with Brentford's set-piece threat, but it also helped his side take control.
Fernandez cut the hosts open for the first time with a pass that set Jackson in behind, although after rounding Flekken, his weak shot was cleared off the line by Zanka. Jackson, though, wasn't to be denied moments later when he rose to head in Malo Gusto's perfect cross.
Chelsea piled forward with Brentford needing the interval as Ben Chilwell's goalbound shot was blocked and then Jackson forced Flekken into a low save.
Brentford were a different side in the second period, pushing higher up the pitch and not allowing Chelsea to dominate possession. It quickly paid off as Reguilon's blocked shot inside the area rolled through to Roerslev to finish.
They almost led two minutes later when Vitaly Janelt hit the foot of the right post, but Chelsea could have easily been ahead too when Cole Palmer put wide after a surging run from Gusto.
It appeared a costly miss when Reguilon's cross from the left popped up off Frank Onyeka in the box and Wissa leapt into the air and acrobatically volleyed home, prompting the Chelsea fans to turn against their manager.
Reguilon nearly wrapped up a victory, climbing over Gusto to head against the left post, but after Flekken had fumbled a shot that forced a Chelsea corner, Disasi planted Palmer's cross into the net.
Poch: I'm not worried about fan backlash
Chelsea manager Mauricio Pochettino said in his post-match press conference:
"For 45 minutes we were very good, we controlled the game. They increased their level of intensity, started to win duels and played more direct. We were not consistent in defending better. When we conceded it changed the game and their belief increased.
"We were the better side but we needed to score in key moments and defend better. After six days and three tough games, it was difficult in the second half to keep the same energy."
On chants wanting him gone: "I've been told but I didn't hear, to be honest. It's normal, we were losing the game 2-1 and they expressed their frustration. Of course, I am responsible, I am the head coach."
Worried about relationship with fans? "I am not worried. We need to accept this relationship. Someone asked me, 'You feel the love from the fans?' No. We need to build our relationship. You build your relationship by winning games but at the moment we are not matching the expectation. Normally in football, you pay with the coach or with the people above."
What if it continues to worsen? "I think the relationship is good. We need to understand fans are emotional. I am fighting with all my sense to try to provide a team with the tools to work, improve, score goals and win games. Today is my 52nd birthday, I know this business very well, but I'm never going to give up. I'm ready to fight tomorrow and the next game. We are going to keep going."
Frank: Fans booing? What the...?
Brentford manager Thomas Frank said in his post-match press conference:
"I would have loved three points, but it was a relatively even game in terms of chances.
"I'm very pleased with the response after a bad performance at West Ham. Today I must say, impressive."
On Brentford fans booing at half time: "I would like to personally speak to the ones who booed. Is that support? We're talking about Brentford vs Chelsea, one of the biggest clubs in the world, we're down 1-0. I know I can't swear but what the..?
"They were brilliant when we got to 1-1 and 2-1, they help us so much. We can't do without [them]. I will fight, the staff will fight, the players will fight but we need them as well, not only when it's going in the right way. When it's not going well we need them even more.
"At 2-2, and I understand we're a little bit nervy, it was very quiet. So maybe it was the ones who booed who didn't have more energy. I don't know."
Opta Stats: Brentford beaten in the air again...
- Since losing their first Premier League encounter against Chelsea in October 2021 (1-0), Brentford are unbeaten in their last five against the Blues (W3 D2), scoring 10 goals and conceding just three.
- Chelsea conceded their third Premier League goal in the opening five minutes of the second half this season, they last shipped more such goals in a single campaign in 2003-04 (4).
- Brentford have conceded 15 headed goals in the Premier League this season, at least three more than any other side in the competition.
- Chelsea's Nicolas Jackson scored his eighth Premier League goal of the season, ending a run of six league games without netting - only Cole Palmer (10) has scored more for the Blues in the competition this season.
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What's next?
Brentford head to title-chasing Arsenal on Saturday March 9, live on Sky Sports. Kick-off 5.30pm.
Chelsea host Newcastle on Monday Night Football on March 11, live on Sky Sports. Kick-off 8pm.