Alexander Isak's thunderous effort, the Swede's fifth league goal of the 2024/25 campaign, fired the Magpies into a deserved lead at St. James' Park before Curtis Jones' strike shortly after the restart found the hosts back on level terms.
Anthony Gordon's composed finish, though, regained United's one-goal cushion after the hour mark but despite Mohamed Salah's brace firing the Reds ahead in the closing stages, Schär's effort in the final minutes salvaged a commendable point for Eddie Howe's side.
The hosts began the contest in strong fashion as Sandro Tonali cleverly evaded the challenge of Alexis Mac Allister on the edge of the box before the Italian midfielder's resulting effort was pushed out by for a corner by Reds goalkeeper Caoimhín Kelleher.
Newcastle goalkeeper Nick Pope produced a key stop to prevent Mac Allister from breaking the deadlock as the Argentine's fierce first-time drive from the edge of the box was pushed out for a corner by the 32-year-old shot-stopper before the South American midfielder hit the woodwork minutes later, firing another teasing effort at goal which clipped the base of the left-hand post.
Jacob Murphy, the sole change from United's 1-1 draw against Crystal Palace last weekend, almost fired the Magpies ahead as the right winger raced onto Isak's perfectly-weighted pass before drilling a firm effort onto the outside of the far left-hand post.
In the 35th minute, Isak broke the deadlock in stunning fashion, collecting Bruno Guimarães' pass before rifling an unstoppable strike from the edge of the box, reaching a speed of 70 miles per hour, into the roof of the net.
Gordon missed a glorious opportunity to double Newcastle's advantage before the half-time break as the Liverpool-born winger capitalised on Joe Gomez's error before racing through on goal but his shot was blocked by Kelleher.
In the 50th minute, however, Newcastle's hopes of a clean sheet were dashed as Jones levelled for the visitors, with the young midfielder arriving onto Salah's teasing pass from the right flank before lifting the ball into the roof of the net.
Newcastle, searching for a first win against Liverpool since December 2015, withstood attacking pressure from the visitors as Darwin Nuñez, who netted a brace in last season's Premier League encounter at St. James' Park, failed to connect to Cody Gakpo's header across the face of goal following Salah's in-swinging cross from the right wing.
In the 62nd minute, Gordon fired Newcastle back in front as the England international raced in behind following Isak's pass and, after cutting inside, cooly placed the ball into the bottom right-hand corner.
Newcastle thought they had extended their lead minutes later as the lively Isak advanced behind the Reds defence before cooly slotting the ball into the bottom right-hand corner but the Magpies striker's effort was disallowed after straying into an offside position.
Pope made a crucial save to deny Jones after a cross from the left flank was flicked on by Dan Burn but the Magpies goalkeeper produced an unorthodox stop, swiping away the Liverpool midfielder's header from close-range.
United's lead was quickly extinguished as Salah equalised for the visitors in the 68th minute. After Trent Alexander-Arnold's initial cross was blocked by Lewis Hall, the substitute's second delivery found the Egyptian forward inside the box, who delicately swept a first-time effort into the far left-hand corner.
Murphy went close to restoring United's lead after beating Kelleher to Gordon's lofted through ball but could only steer his first-time effort wide of the left-hand post.
Salah struck the woodwork for the visitors after his strike inside the box clipped the top left-hand corner of the bar, to the delight of the Magpies supporters, but the home crowd were deflated in the 83rd minute as Salah sent Liverpool ahead, collecting Alexander-Arnold's pass on the turn before directing his effort into the bottom left-hand corner.
United went in search of a late leveller and were rewarded as Schär equalised for the hosts, arriving at the back post from Guimarães' inviting free-kick from the right flank before the stretching Swiss defender managed to slide his effort from the left byline into the net.
In the final seconds of stoppage-time, Pope quickly threw the ball towards Isak on the halfway line but referee Andy Madley brought an abrupt end to the six-goal thriller before the counter-attack could take place to the frustration of the home supporters.
Newcastle United: Nick Pope, Tino Livramento, Fabian Schär, Dan Burn, Lewis Hall, Bruno Guimarães, Sandro Tonali (Sean Longstaff 87), Joelinton (Joe Willock 87), Jacob Murphy (Harvey Barnes 74), Anthony Gordon (Callum Wilson 87), Alexander Isak.
Subs not used: Martin Dúbravka, Lloyd Kelly, Matt Targett, Miguel Almirón, Will Osula.
