Luton looked on course for all three points when Elijah Adebayo sent them 4-2 ahead in the 62nd minute of what was a Premier League classic, but Kieran Trippier made it 4-3 in the 67th minute before Harvey Barnes netted the leveller six minutes later.
The result has left Newcastle, who led 1-0 and 2-1 on home soil, in ninth position in the Premier League table, boasting 33 points from 23 matches, while Luton move into 16th position, with the promoted outfit one point ahead of 18th-placed Everton in England's top flight.
Newcastle, backed by a vocal home support, were on the front foot from the first whistle, and the breakthrough arrived in just the seventh minute of the clash at St James' Park.
Sean Longstaff was the player to open the scoring, with the midfielder picking out the back of the net with an emphatic finish after Kieran Trippier had delivered a dangerous cross into the Luton box.
Chiedozie Ogbene was threatening for the visitors, and he delivered a brilliant low cross into the Newcastle area in the 11th minute, but there were no takers.
Carlton Morris then headed into the gloves of Newcastle goalkeeper Martin Dubravka from a corner, and the warning signs were certainly there, with Luton threatening to level.
The equaliser came in the 21st minute, with Gabriel Osho heading into the back of the net after Morris had nodded a free kick from Ross Barkley into a dangerous area.
Newcastle were back ahead in the 23rd minute, though, with Longstaff finding the corner after Luton goalkeeper Thomas Kaminski had kept out a strike from Anthony Gordon.
The Magpies had a chance to score a third 10 minutes before the end of the first period, but Gordon's shot from a Jacob Murphy cross was brilliantly blocked by Teden Mengi, and Luton then managed to level the scores in the 40th minute through Barkley, who tapped home from close range after Dubravka could only palm a cross from Alfie Doughty straight to the midfielder's feet.
Newcastle had a golden chance to make it 3-2 early in the second period, but Kaminski did brilliantly to just clear a Murphy cross ahead of Bruno Guimaraes, who would have had a tap-in.
Murphy was dangerous and had another opportunity in the 51st minute, but his effort was wide.
Luton were then awarded a penalty when Dan Burn unfairly challenged Ogbene inside the box, with VAR overturning the initial decision of a free kick, with the contact taking place in the penalty area.
Morris had to take his penalty twice, with the first effort being chalked off for players being out of position, but the second one counted, with Luton leading 3-2 at St James' Park in the 59th minute.
The visitors then incredibly score a fourth in the 62nd minute through Adebayo, with the forward drilling the ball into the bottom corner after meeting a clever pass from Barkley.
Newcastle answered back in the 67th minute, with Trippier finding the corner with a composed finish after a cross from Guimaraes had caused Luton a problem.
Fabian Schar had a shot deflected behind for a corner in the period that followed, with Luton's goal coming under increasing pressure during an incredible game.
Newcastle managed to make it 4-4 in the 73rd minute through Barnes, with the attacker brilliantly rolling the ball into the bottom corner after driving into space just outside the Luton penalty box.
Dubravka did well to keep out a strike from Adebayo soon after, before the Magpies goalkeeper denied Jacob Brown in the spell that followed.
Murphy just failed to make contact on a dangerous cross from Guimaraes in the latter stages, and both teams were pushing for what would have been an extraordinary winner, but the points were ultimately shared in a 4-4 draw.
Newcastle will continue their league campaign away to Nottingham Forest next Saturday, while Luton will be in action on the same afternoon against Sheffield United at Kenilworth Road.