Going into the match on Saturday, their first since the 3-0 win over Chelsea, Everton were in a great position to try and end a long drought without competing in Europe, if they could maintain their solid recent form and momentum.
Travelling to North London to face Brentford, though, was a daunting task given how well the Bees have again played in this campaign and the fact that they beat the Toffees easily at the Hill Dickinson Stadium earlier in the season.
In addition, Everton do not have a good record in the capital, and so needing to get points and avoid defeat at one of their rivals for a European place, made this an even more challenging fixture.
The away team could hardly have made a worse start with Jordan Pickford bringing down Brentford's dangerous wide man, Kevin Schade, in the box just two minutes in, and Igor Thiago converted the spot kick to make it one-nil.
Everton did not panic and came back into the game well, creating several good chances before finally getting the equaliser they deserved through Beto's header from Idrissa Gueye's cross.
It was a competitive match with both sides determined to find a way to win. Brentford hit the woodwork twice, either side of half-time, and the Blues had to dig in and defend well for periods of the contest, although they never looked out of it and always retained a threat.
After the home team had regained the lead again, through Thiago -- how much the Toffees could do with a striker of his productivity -- it looked like Everton's excellent away form this season would not continue in London.
However, they kept fighting, and Kiernan Dewsbury-Hall, a player who has so often popped up to score crucial goals this season, did it again.
The ex-Chelsea man slotted home in added time after previously missing a good chance, to ensure the Toffees got another point on their travels.
Getting a draw at a talented team like Brentford is certainly a solid result and keeps Everton very much in the hunt for that desired European place next season.
But the Blues have several tough fixtures still to play, starting with the first-ever Merseyside derby at the Hill Dickinson next weekend.
Other results will obviously matter too, with the Toffees' rivals Fulham and yesterday's opponents facing each other the day before the derby.
Both Everton and the Bees also have to play championship-chasing Manchester City in early May, so it looks almost certain this race will go down to the wire.