Liverpool thought they had done enough to secure a vital win that would preserve their nine-point advantage at the top of the table after twice coming from behind, with Mohamed Salah putting them 3-2 ahead with just seven minutes remaining.
But Schar volleyed in from a free-kick that Caoimhin Kelleher failed to claim, ensuring a well-earned point for Newcastle.
Liverpool came into the match off a brilliant victory over defending champions Manchester City, leaving them nine points clear at the summit heading into the midweek fixtures.
However, they struggled against a Newcastle side who showed determination from the very start.
Jacob Murphy came close early on, hitting the post with a shot, before Alexander Isak stunned the visitors with a spectacular long-range goal.
Anthony Gordon almost made it 2-0 soon after a Joe Gomez mistake, but Kelleher produced a crucial save.
That save looked pivotal when Liverpool equalised in the second half through Curtis Jones’ powerful finish from Salah’s assist.
Yet, Gordon sparked wild celebrations at St James’ Park when he cut inside a defender and saw his shot slip past Kelleher.
Salah responded with an equaliser before confidently putting Liverpool 3-2 up, but Schar’s late strike left both teams sharing the spoils.