Substitute Vitaly Janelt scored a late equaliser as Brentford denied Everton a first Premier League win of the season.
Anthony Gordon had put the Toffees on course for a much-needed victory, firing home a well-taken opener after 24 minutes.
Brentford struggled to breach the visitors' defence, and hit the woodwork three times on an afternoon that appeared destined to end in frustration.
But Janelt popped up with the equaliser six minutes from time, converting from close range after Keane Lewis-Potter's near-post flick-on from a corner.
Bees boss Thomas Frank later said: "I'm very pleased and proud of our team. The players are amazing and showed top mentality. The amount of chances we created today was incredible.
"How we dominated it and controlled the game throughout but didn't win, that will be a big mystery.
"We have shown that we like to make substitutes and have good players who can change games. I 100% feel like we should have won.
"That was a nine out of 10 performance."