Igor Thiago made history by scoring his 21st goal of the Premier League season but it wasn't enough as Everton snatched a stoppage-time point from Brentford.
A win for either side would have meant that they would move up alongside Liverpool in fifth, putting them within touching distance of an unlikely Champions League spot with a month left in the campaign.
The hosts thought that would be them after Thiago's historic double, but a Kiernan Dewsbury-Hall stoppage-time equaliser meant both sides missed their chance.
Brentford made the dream start as Kevin Schade raced through on goal and was taken out by Jordan Pickford inside the opening two minutes.
Thiago, fresh off his first goal for Brazil during the break, made no mistake from 12 yards to score his 20th Premier League goal of the season and tie Ivan Toney and Bryan Mbeumo for the club record in the competition.
While it was a slow start from the Toffees, they grew into proceedings and forced Caoimhin Kelleher into a remarkable double save just before the half hour mark. However, they wouldn't have to wait too much longer to pull level as Beto clinically headed home moments later despite protests for a foul on Keane Lewis-Potter in the build-up.
Schade nearly went from provider to goalscorer as his header from a set-piece cannoned off the bar from a corner which was won thanks to a sharp save from Jordan Pickford to keep out Mathias Jensen.
The hosts hit the woodwork again early in the second half via the head of Collins, while the Toffees were thwarted once more by Kelleher who denied both Iliman Ndiaye and Dewsbury-Hall impressively.
Cometh the hour, cometh the man as Thiago broke the record in fortuotous fashion as Michael Kayode's toepoke deflected off the striker, who was trying to get out the way of the shot, and beat the prone Pickford.
It seemed that would be enough for the win, until Dewsbury-Hall showed incredible composure to slot home in the 91st-minute meaning that both remain in seventh and eighth respectively.
Brentford boss Keith Andrews speaking in his post-match press conference on Igor Thiago:
"I think the biggest thing for Thiago this season was staying fit and playing as many minutes as he has. That's your first target.
"The reality is you never know. Anybody who says any different, isn't being entirely honest. We always knew he had brilliant attributes. I think he's selfless in the way he plays the game for us. The goals obviously get all the attention.
"But his overall performance levels continue to get better and better and he's constantly evolving his game. I think he's proven to be a very, very special player.
"I think there's been some outstanding strikers here already. I think what he is, is an all-round centre-forward.
"It's probably wrong for me to put him in a bracket against the rest, because I was a big fan of all those players that you're probably thinking of. But Thiago is obviously pretty special for me."
Everton midfielder Kiernan Dewsbury-Hall speaking to Your Site after his late equaliser at Brentford:
"A bit of a rollercoaster of a game. We knew it was going to be a tough game there.
"They've got strengths that they play to really well. Probably on the balance of things, maybe a draw is the fair result.
"The fact we came from behind twice shows the mentality of these lads.
"We'll never give up until the final whistle. So it was nice to score a late goal and at least take something away from it.
"It's cliché as it is, if you don't win, try not to lose. And we did that and it's pleasing, like I said, to react from going behind twice. So look, we could come to the end of the season and that's a massive point.
"Let's take it into the next game, a massive game for us next week. Hopefully, we can try and get a good result."
Everton boss David Moyes speaking to Your Site about next week's Merseyside derby:
"We'll get ready for it. The next one's Liverpool, which will be a brilliant, brilliant game for all the Evertonians.
"You know, first time we've had Liverpool in the new stadium.
"So we'll all be looking forward to it. We're in a much healthier position than we've been in for many years.
"So we'll go to the game. You know, got a lot to be positive about and think about. So hopefully we can go to the game and do the best we can."
