The loss to a team now only one point behind the Whites has heightened fears of getting dragged into a relegation scrap for Leeds, whose next three games are now against Manchester United, Liverpool and Tottenham.
Short of a surprise result in the matches coming up it looks like an uncomfortable time ahead for Bielsa's men as it is likely to get worse before it gets better for them.
And after picking up just one point from games against Newcastle, Aston Villa and now Everton they cannot go into these tough looking games with any great confidence.
Leeds did hit the woodwork twice through Rodrigo at Goodison Park, but they were comfortably beaten by a team who had not won a Premier League game in 2022 - but who, unlike the Whites, signifcantly strengthened in the recent transfer window.
Tactically Bielsa admitted he got it wrong with the decision to a field a back three and Mateusz Klich as the holding midfielder in the continued absence of key man Kalvin Phillips.
“It was a fair result,” said Bielsa.
“It was difficult to defend. Second half we defended a bit better, but could not attack. We did not defend well in the first half, but we created some danger.
"Second half we defended better apart from at the end, but we did not create danger. The result was fair.
“The position of Mateusz Klich was an error on my part. A midfielder in front of three centre-backs, he had to defend too much. He could not do what he does best, which is make runs in attack.
“Sincerely, I assigned a task to him which was going to be difficult for him. I don't think it was so much it was difficult to retain the ball, but more difficult to recover it."
Bielsa also confirmed that the decision to take off star player Raphinha at half-time was tactical as the Brazilian ace was not injured.
He added: “I decided that Daniel James should take over his role on the right and Tyler Roberts take over in the centre. He is not injured.”
Leeds were behind from the tenth minute when Seamus Coleman headed home from close range after Dominic Calvert-Lewin's effort had been deflected.
By then the Whites had already lost another player to injury with Stuart Dallas having to be replaced by Leo Hjelde.
Everton were pushed back for a spell and the first of Rodrigo's unlucky efforts saw him hit the crossbar with a well struck volley.
But it was the hosts who looked livelier and went two up on 25 minutes as Anthony Gordon's corner was headed home by Michael Keane - United's well publicised weakness from set pieces striking again.
The visitors were chasing shadows again when Gordon went close to adding to their woes and Alex Iwobi went close.
In a typically pacy game involving Bielsa's side the Whites almost pulled a goal back, but Rodrigo again saw a well struck shot hit the crossbar with the home keeper beaten.
The second half saw the pace slow down as at Villa a few days earlier and the game began to get broken up. United had plenty of possession with Adam Forshaw on to improve the midfield, but with the out of sorts Raphinha taken off at half-time they lacked quality in key areas.
They struggled to create anything of note, aside from shots by Dan James and Rodrigo that did not trouble keeper Jordan Pickford.
Illan Meslier kept the Whites in the game with a save to deny Gordon, but he could do nothing to prevent the hosts from sealing the game 10 minutes from time with their third goal.
Substitute Delli Ali was given space and time to get a cross in and it was perfect for Richarlison, whose shot took a small deflection off Gordon to end up in the back of the net.
There was no sign of any late comeback from a deflated Leeds team and the defeat would have been bigger had it not been for a superb late save by Meslier as he acrobatically kept out an effort from another home sub, Salomon Rondon.
(Coleman 10, Keane 23, Gordon 78)
Saturday, February 12, 2022
Everton: Pickford; Coleman, Holgate, Keane, Kenny; Allan, van de Beek, Iwobi; Gordon (El Ghazi 81), Richarlison (Rondon 86), Calvert-Lewin (Alli 72).
Leeds: Meslier; Llorente, Koch, Struijk; Ayling, Klich (Forshaw 45), Dallas (Hjelde 8); Raphinha (Roberts 45), Rodrigo, Harrison; James.
Referee: Graham Scott