Hayden struck four minutes of added time after getting to the end of a cross to secure the hardfought win for Newcastle.
Chelsea have now lost eight Premier League games this season and remain fourth on 39 points in the league table.
While Newcastle are 12th on 29 points on the log.
Newcastle had the first big chance in the 21st minute as a cross from the right was met by Joelinton but his header crashed off the bar and is cleared.
On 33 minutes Chelsea also hit the crossbar through Tammy Abraham following a flick from N’Golo Kante but the flag was already up for offside.
Just a minute later Martin Dubravka came out of his goal to deny Kante from close range.
Chelsea’s first big chance of the game fell to Abraham in the 72nd minute as went round Dubravka but missed the target.
In the 79th minute Chelsea came very close through Abraham as his effort sneaked past Dubravka but Matt Ritchie cleared off the line.
But in the 94th minute former Arsenal midfielder Isaac Hayden got a slight touch on Saint-Maximin’s cross to win it for Newcastle.
By James Agberebi
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