Liverpool extended their lead atop the league table to seven points over second-placed Arsenal with what had been their game in hand, while Everton climbed to 10 points above the drop zone in 15th.
And after 131 years of Goodison derbies, the draw was a fitting ending with the final tally totalling 41 wins apiece and 38 draws.
Everton's Beto had the old stadium shaking with his 11th-minute goal. The jubilation lasted all of five minutes as Alexis Mac Allister levelled.
Both sides had chances in a chaotic match and Salah struck to give Liverpool the lead in the 73rd minute against the run of play.
Liverpool looked poised for victory when Tarkowski struck in the 98th minute with a blistering shot into the top corner. Scores of fans piled onto the pitch before a lengthy VAR review ruled the goal was onside.