Jurgen Klopp’s men now trail champions Manchester City by a point at the top of the Premier League with nine games remaining.
Fabinho was also guilty of wasting a big opportunity 21 minutes from time as Lucas Digne cleared when the Brazilian took an age to control Virgil van Dijk’s knockdown.
Everton remain without a win in the Merseyside derby stretching back to 2010, but may have done enough to stop their local rivals from winning the title for the first time in 29 years.
Salah has now scored just once in his past six matches and wasted by a distance the best chance for either side from the sort of situation he finished with ease in a 44-goal debut season at Anfield last year.
Pickford was at fault for Liverpool‘s 96th minute winner when the sides last met in December, but the England number one went some way to making amends by standing tall to block as Salah bore down on goal before Seamus Coleman threw himself in the way of a follow-up attempt from Jordan Henderson.
That was a rare glimpse of goal in a first-half which generated plenty of excitement and atmosphere but little in the way of goalmouth incident.
Everton have endured a disappointing season after spending big in the summer to back Marco Silva and their lack of quality on the ball showed despite their commitment and desire to close Liverpool down.
The hosts at least opened the second-half with slightly more urgency, Dominic Calvert-Lewin rising to meet an early Lucas Digne corner, with a header that was saved comfortably by Alisson Becker.
At the other end, Salah spurned another chance when the ball broke his way off Kurt Zouma, but the Egyptian took a heavy touch and allowed Keane to make a stunning recovery tackle.
Klopp had seen enough by just after the hour mark and brought on James Milner and Roberto Firmino, recovered from his recent ankle injury, in a bid to turn one point into three.
The Brazilian almost made an instant impact, marauding forward with Salah, but his cross proved a little long for Sadio Mane who could only head back across goal harmlessly.
Van Dijk was again peerless in his defensive duties and nearly set up the winner had Fabinho been sharper to fire home the Dutchman’s knock down.
Roared on by an increasingly vocal home crowd, Everton also created some late chances with a cross from substitute Richarlison coming within inches of finding the sliding Bernard.
However, for the third time in Liverpool‘s last four matches the game ended scoreless to hand City the initiative in the title race.