So a draw was secured which kept the unbeaten streak going that Everton had recently established, and extended it to five games in a row.
However, for most of the match it did not look as though the Blues would get anything from the fixture as the team turned in another lacklustre, tentative and disappointing performance.
Fulham were overall the better side, although the home team did have a couple of early chances with Idrissa Gueye hitting the woodwork and Dominic Calvert-Lewin's follow-up finish being ruled out.
But the Cottagers had more control and played the better football, while they also had a few good opportunities to open the scoring through Adama Traore and summer signing Emile Smith-Rowe.
It was not much of a game for the TV viewers tuning in on a Saturday night and once again highlighted the problems and issues with this Everton side.
Sean Dyche picked what has become his favoured team over recent weeks with Jarrad Branthwaite still not starting in central defence as Micheal Keane continued there and Iliman Ndiaye again confined to the wing.
This formation has brought improved results over this five-game period, but it continues to be frustrating to watch and I think it is failing to get the most out of the Toffees best players.
Too often - as we have seen so many times over the last eighteen months and longer - Everton resorted to long balls hoofed up-field aimlessly with Calvert-Lewin mostly chasing lost causes and Ndiaye largely unable to affect the game.
In some ways you can make a case for why Dyche continues to set up his side to play this way given how fragile the team seened to be early on in the season and how easily it was conceding soft goals.
He was dealing with unexpected lapses defensively mainly caused by injuries to Branthwaite and full-backs Seamus Coleman, Nathan Patterson and Vitalii Mykolenko.
But, on the other hand with most of his absent players now more or less fit again, the Blues have to find a way to expand their game and start offering more of a consistent threat in front of goal, especially at home.
This of course is the final campaign to be played at the Grand Old Lady and the Toffees have so far only won a single match this season at the ground they have called home since 1892.
Everton's players seem inhibited and unable to produce their best when playing at Goodison Park and this continued today.
I believe that Dyche has to tweak his approach and consider something like reverting to a 4-3-2-1 with Ndiaye alongside Dwight McNeil (if the manager wants to continue using the former Burnley man who came off late on in that way) with both operating behind Calvert-Lewin.
Ndiaye is far and away the Toffees most effective and dangerous forward who offers something different with his pace, skill and willingness to take on defenders.
Once he got more involved later in the second half, Everton did improve with his contribution starting the move for the equaliser.
Ironically and of course predictably, it was Alex Iwobi - an ex-Everton player - who opened the scoring for the Cottagers.
Iwobi finished a neat move from the visitors after the hour mark and then refused to celebrate in front of the Goodison faithful, although let's be honest some of the home support had often been very critical of him.
Time ticked on and it looked as though the Blues were heading for a defeat that would snap their good run of results.
Everton rarely appeared to be likely to break through and Dyche threw on his Portuguese striker Beto in what looked to be a frankly desperate move given his lack of goals since signing last year.
Beto though was to be the hero for the home team as he climbed to meet Ashley Young's cross and head the ball into the back of the net in the ninety-fourth minute.
A draw is obviously better than a defeat, but although it might feel a little like a win after being behind for so long, it is another two points dropped that could prove important.
Now comes two crucial away matches at struggling Southampton and West Ham before the next international break.