Local boys Steven Taylor and Jack Colback put the Magpies ahead but Paul Dummett's shambolic own goal and Danny Ings' strike had Burnley level on each occasion.
Moussa Sissoko restored the Magpies' advantage but George Boyd's low angled drive secured a point for the Clarets.
Tottenham inflicted an astonishing 5-3 defeat on Chelsea to allow Manchester City to move level with Jose Mourinho's men at the top of the Barclays Premier League.
Despite Diego Costa's opener, Spurs led 3-1 at half-time after goals from Harry Kane, Danny Rose and an Andros Townsend penalty.
Kane extended the lead to 4-1 and though Eden Hazard gave Chelsea some hope, Nacer Chadli scored a fifth for Tottenham.
John Terry's late consolation at least prevented Manuel Pellegrini's reigning champions moving top on goal difference, with they and Chelsea sharing identical records after Frank Lampard earlier marked the extension of his City stay by grabbing the winner in a 3-2 victory over Sunderland.
The game at the Etihad Stadium burst into life when Yaya Toure rifled City into the lead shortly before the hour mark and Stevan Jovetic back-heeled a second.
Jack Rodwell's header and a penalty from fellow City old boy Adam Johnson got Sunderland dramatically back on terms but ex-Chelsea star Lampard, on for Jovetic having extended his loan from New York City FC, snatched the winner.
Liverpool also let a winning position slip as Leicester came from 2-0 down to draw 2-2 at Anfield.
The hosts led through two Steven Gerrard penalties but two goals in three minutes, from David Nugent and Jeff Schlupp, levelled matters.
Southampton remain in the top four after an excellent 2-0 win over nearest pursuers Arsenal.
Sadio Mane beat Wojciech Szczesny from a tight angle for the first goal and if the Poland goalkeeper's positioning was questionable on that occasion, his panicked hack clear amid defensive confusion allowed Dusan Tadic to poke home the second.
Manchester United were perhaps fortunate to escape with a 1-1 draw from their lunchtime encounter with Stoke.
Man City 3 - 2 S'land
Hull City 2 - 0 Everton
A Villa 0 - 0 C Palace
Stoke 1 - 1 Man Utd
Newcastle 3 - 3 Burnley
Liverpool 2 - 2 Leicester
QPR 1 - 1 Swansea
West Ham 1 - 1 W Brom
Tottenham 5 - 3 Chelsea
So'ton 2 - 0 Arsenal
The Potters took an early lead when Ryan Shawcross deftly turned in Peter Crouch's header but Radamel Falcao equalised for United.
Stoke had penalty appeals rejected when Crouch's header struck Chris Smalling's arm and when the former England striker hit the post and Geoff Cameron may have been impeded as he challenged for the rebound, but they had to settle for a point.
Sixth-placed West Ham drew 1-1 with West Brom.
Diafra Sakho headed the hosts in front from Aaron Cresswell's cross but Saido Berahino exchanged passes with Stephane Sessegnon before slotting home the equaliser as new Baggies boss Tony Pulis watched on from the stands.
Struggling Hull won 2-0 to inflict a fourth successive league defeat on Everton.
Ahmed Elmohamady headed in fellow wing-back Liam Rosenior's cross and Nikica Jelavic sprung the offside trap to lob goalkeeper Joel Robles before Everton lost Antolin Alcaraz to a second yellow card late on.
Swansea left it late to earn a 1-1 draw against QPR at Loftus Road.
Leroy Fer's 25-yard rocket gave Rangers a 20th-minute lead and Swansea ended the game with 10 men when Wayne Routledge was sent off for an angry reaction to a late tackle from Karl Henry - for which the midfielder was booked.
But they snatched a stoppage-time equaliser when substitute Wilfried Bony produced an opportunistic finish.
Aston Villa and Crystal Palace - the latter widely expected to announce Alan Pardew as their new manager - played out a goalless draw enlivened only by Yannick Bolasie's spectacular effort against the crossbar for the visitors.