Dango Ouattara was the penalty villain for Brentford as his failed Panenka in the shoot-out cost the Bees - and sent West Ham to the FA Cup quarter-finals at their expense.
After Jarrod Bowen and Igor Thiago got two goals each in normal time - with nothing decided in extra-time - Ouattara tried to chip Alphonse Areola down the middle but the West Ham goalkeeper read it and stood still to gather easily.
On the other side of the coin, West Ham emphatically smashed all of their penalties with poise - as Konstantinos Mavropanos scored the winning spot-kick to set up a last eight contest with fellow Premier League relegation rivals Leeds in early April.
A superb first half saw both teams go for it - leading to three goals in the space of 15 minutes.
Brentford missed early chances through Jordan Henderson and Michael Kayode before West Ham made them pay as Bowen tapped home his first of the game after picking up a knock-down from Matheus Fernandes' cross.
Brentford found a way back into the game through a likely source. Nathan Collins' goalbound header from a throw-in routine was diverted in by Igor Thiago, who in chesting home, notched his 20th goal of the season in all competitions.
But the Bees would find themselves behind straight away as from the kick-off, Adama Traore was brought down by Kayode and, despite referee Andy Madley somehow not spotting the clear trip, VAR sent him to the monitor to award a spot-kick. Bowen dispatched it with ease.
Madley and VAR would be busy again before the half's end as Kevin Schade went down under Fernandes' trip in the area. Replays showed the West Ham midfielder got the slightest touch on the ball before standing on Schade's foot, with VAR not biting on the penalty appeals.
"Yeah it's a penalty," said Brentford boss Keith Andrews after the game.
Asked if he can understand why it wasn't given, he replied: "Not really no. There was clear contact on his foot.
"I can't see how it can't be overturned by VAR when we've had one that was overturned and got re-refereed. From where Andy [Madley] was on the pitch, he looked at our one and didn't give it? So yeah, strange."
But there would be a second penalty of the game late on after Kayode was pushed by half-time substitute Crysencio Summerville at the back post. Ref Madley did not need VAR to give that one, with the shove clear to see.
Thiago stepped up to pull Brentford level for a second time, with Keane Lewis-Potter then missing a chance to win it before the 90 minutes was up as he flashed an effort wide.
Extra-time continued to provide lively moments. The fresh legs of Romelle Donovan and Callum Wilson failed to convert decent chances, while Summerville - who was booked for conceding the Brentford penalty - avoided a second yellow card for a clear trip.
Axel Disasi nearly won it with virtually the last kick of the game as his long-range effort flew just over the bar, and that brought penalties - where Ouattara's dreadful moment from 12 yards decided it.
Brentford head coach Keith Andrews:
"I'm not annoyed at all. The easiest thing for a footballer to do is to not take a penalty. It takes unbelievable courage on a stage like that to take a penalty.
"I despise the culture around players that have missed penalty kicks. We're talking about national heroes who have done it. They have been ridiculed, persecuted. I think it's disgusting.
"It takes serious courage to do that [take a penalty]. He practices that technique a lot. If it goes in, everyone's raving about him. So Dango will get the absolute support he needs from us and everybody attached to him."
West Ham captain Jarrod Bowen to TNT Sports:
"We haven't been good enough this season, but we're coming into the real business end of it now. There's a big game coming up on Saturday, we're into the quarter-finals of the FA Cup, and things are on the up for us. But we have to keep doing it, keep demanding it, keep raising the level.
"I go back to the QPR game [in the third round] where I don't want to say our season started, but that was the chance to turn it around and give us confidence and belief.
"We've done that in the Premier League and tonight was the same thing. We had to put in a good performance and we knew it'd be a tough game. Every FA Cup game we've had has gone to extra-time now. But we want to get to the final, we want silverware at this club.
"It's a dream of mine to win it [the FA Cup] and we've got a long way to get there, but tonight is a big night for everyone involved."
West Ham head coach Nuno Espirito Santo to TNT Sports:
"Our fans deserve this moment of joy. They way they support us through bad times, the way they keep supporting the team, thank you for that. The team did a good job.
"The players are delighted in the dressing room. Tired, but delighted. A tough one against an amazing team. We controlled them and contained them with a lot of chances, I'm happy that the game came to us in the end.
"Now we have to rest. Knowing Saturday we face a tough one [against Man City]. But in our stadium, our boys are playing in the London Stadium. The atmosphere is good. It's a tough one, we want to compete. And our performance will require the best from all of us."
