It meant that it was three wins from three as Maurizio Sarri continues his fine start with the Blues but it was not without trouble as Joselu answered back for the hosts after Hazard had given the Blues the lead.
The visitors had dominated much of the game, however, it took a dubious penalty and an own-goal for the London side to get their first win at St. James’ Park since 2011.
Rafa Benitez’s side were completely dominated by the possession from the Blues, however, they had managed to keep themselves in the game for the majority of the 90 minutes.
Chelsea dominate but find it difficult to make the most of the possession
Chelsea had over 80% of the ball, however, their failure to make the most of their chances could have cost them during the game on a different day.
It was not until the latter part of the second half when Marcos Alonso was brought down in the penalty box from a challenge by Fabian Schar, although there was an opinion that the defender had won the ball before bringing the Spaniard down.
The Switzerland international slid in and appeared to win the ball first, however, he gave the referee a decision to make with the type of challenge and he decided to point to the spot.
Eden Hazard comfortably despatched the ball from 12 yards out, however, the Blues were left looking for a second goal to secure the three points with just under ten minutes remaining.
Newcastle make life difficult
DeAndre Yedlin managed to dig out a cross into the Blues' penalty area with Joselu managing to get onto the end of the ball and heading home past Kepa Arrizabalaga.
However, that goal was not without its controversy, as the Newcastle right-back appeared to elbow Olivier Giroud when he ran towards making his cross.
Despite that, Chelsea boss Sarri could not be happy with the way his side defended.
David Luiz was caught on his heels and was easily beaten by Joselu for the ball, leaving Chelsea on the edge of taking just a point from the game that they had dominated in.
However, the Blues stepped it up a notch and managed to get a winner in the dying minutes of regular time when Alonso had a shot that was turned into the net by Yedlin.
Newcastle will have a tough encounter with Nottingham Forest in the League Cup in midweek before they travel to Premier League champions Manchester City next Saturday.
Chelsea will host AFC Bournemouth at Stamford Bridge as Sarri looks to make it four wins from four.