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.
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.