Tomas Soucek's second-half strike earned West Ham a point at Brentford after Bryan Mbeumo scored another quickfire goal for the hosts in the first minute.
For the third Premier League game in succession Brentford scored with less than 60 seconds on the clock, with Mbeumo curling a volley out of Alphonse Areola's reach.
Despite falling behind so early, West Ham remained positive and created the lion's share of the chances in the opening 45 minutes.
Jarrod Bowen, Michail Antonio and Mohammed Kudus all had opportunities, although only the latter managed to find the target.
Brentford seemed happy to sit back and soak up pressure after such a bright start, with their next effort at goal coming in the 34th minute when Mbeumo headed over the bar.
West Ham's pressure finally told shortly after half-time when Soucek, brought into the starting XI for the suspended Edson Alvarez, pounced on a loose ball to slot in from close range.
With the game finely poised, Brentford started to control possession and eventually worked their way into some positive positions.
Yehor Yarmoliuk went closest to re-establishing a lead for the home side but his shot was saved.
West Ham forced Brentford to defend deep in the final 10 minutes and the visitors almost snatched a winner when substitute Crysencio Summerville's shot from a tight angle was deflected on to the roof of the net.
The draw keeps Brentford 12th in the Premier League table, while West Ham remain 14th.
Brentford lacking killer instinct
Scoring early is a great habit to have and Brentford are becoming very accustomed to doing just that - they are the first team in history to score in the opening minute in three consecutive Premier League games.
Mbeumo, who netted after just 23 seconds in last Saturday's 3-1 defeat at Tottenham, was celebrating a fine opener with only 37 seconds gone today, while Yoane Wissa needed a mere 22 seconds to register in the 2-1 loss at Manchester City on 14 September.
But, just as was the case in the defeats at Spurs and Manchester City, Brentford failed to kick on and were left counting the cost.
Only Mbeumo (5) and Wissa (3) have scored in the Premier League for the Bees this season and the latter is expected to be sidelined with an ankle injury for about two months.
The Gtech Community Stadium has provided solace for Thomas Frank's side in the opening weeks of the season - winning their previous two outings on home soil - while they are yet to yield a single point on their travels, albeit having played at Liverpool, City and Spurs.
It is far too early to put Frank under the spotlight, considering the Dane has helped to establish the club, who were playing League Two football in 2009, as a regular fixture in the Premier League.
However, the departure of Ivan Toney this summer - top scorer in three of the past four seasons - and the absence of Wissa has left the Bees looking a little toothless in attack.
There are concerns defensively, too. Brentford are yet to keep a clean sheet and have dropped 38 points from winning positions since the start of last season - the most of any team currently in the division.
Winless streak continues for West Ham
Unlike the man in the opposite dugout, West Ham boss Julen Lopetegui does not have credit in the bank, having only taken charge of the club in the summer.
The Spaniard spent more than £150m in the transfer market but has delivered just one league victory.
After a torrid start, Lopetegui would have been pleased to see the Hammers settle into a rhythm and dominate possession - even if it did not lead to an equaliser during a frustrating opening 45 minutes.
Lopetegui showed courage to make two substitutions at half-time, introducing Paris-St Germain loanee Carlos Soler and defender Konstantinos Mavropanos for Kudus and Emerson.
West Ham looked more balanced after the break and it did not take long for them to haul themselves level.
A neat passage of play on the edge of the box, which included a backheel from Bowen, eventually saw the ball bounce through to Czech Republic midfielder Soucek to bundle in from six yards.
West Ham have not tasted victory in the league since 24 August but they almost snatched three points at the death with Soler hooking a volley towards goal and forcing Mark Flekken into a full-stretch save.
Referee Simon Hooper blew for full-time rather than allowing West Ham to take a corner kick, leading to protests from players and manager Lopetegui.
The Hammers return to home soil next time out with newly promoted Ipswich visiting on Saturday, 5 October (15:00 BST).
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