The Blues dominated possession for long periods but failed to capitalize and were undone in the 94th-minute when Hayden climbed above Antonio Rudiger to meet Allan Saint-Maximin’s cross to head past Kepa Arrizabalaga.
With Sheffield United, Arsenal and Tottenham all dropping points earlier in the day and both Manchester United and Leicester not in action until tomorrow, the Blues had a chance to cement their place in the Champions League places.
However, Frank Lampard’s side failed to create many clearcut openings and the sting in the tail here leaves Chelsea only five points above fifth-placed United having played a game more.
Lampard made just one change to the team that beat Burnley last weekend with N’Golo Kante replacing Ross Barkley in midfield, something of a gamble given he had been continuing to manage a hamstring problem.
Newcastle was content to sit deep with a five-man defense when not in possession with the Blues left to probe for a way through.
Jetro Williams was stretchered off injured inside the opening 15 minutes at the end of a long delay which only contributed further to the truncated feel, the Blues only sporadically able to cause problems despite monopolizing the ball.
Newcastle’s ambition was limited but they almost took the lead after 21 minutes when Joelinton met a cross from the right eight yards out with a firm header which cannoned back off the crossbar.
Tammy Abraham fired over a few minutes later as Chelsea continued to try and engineer a clear opening. That eventually came from Reece James, who curled an excellent pass in behind the Newcastle defense for Kante but his low drive was turned behind smartly by Martin Dubravka.
Federico Fernandez headed over as another cross from the Newcastle right, this time from Jonjo Shelvey, exposed weaknesses and although Chelsea began to up the tempo before the interval, they only had a Mason Mount free-kick deflected wide to show for it.
Chelsea briefly improved more tangibly at the start of the second period. Willian dragged a shot wide to waste a promising counter-attack before Cesar Azpilicueta drilled a 20-yard effort straight at Dubravka.
Space was beginning to open up but they struggled to capitalize, allowing Newcastle to regroup, prompting Lampard to replace Mount with Barkley for the final 23 minutes.
Moments after coming on, Barkley’s pass was intercepted by fellow substitute Sean Longstaff but into the path of Abraham, who failed to steady himself in steering a low shot off target with Dubravka sprawled at his feet.
Abraham almost found the breakthrough with 11 minutes remaining as Azpilicueta turned Jorginho’s pass into his path but his effort was scrambled clear.
It would be Abraham’s final contribution as Lampard sent on Michy Batshuayi but another substitute, Emerson Palmieri, almost won it when his low drive was deflected just wide after Willian’s cross had been cleared into his path. Instead, it was Hayden and Newcastle who had the last laugh.