Newcastle boss Rafael Benitez had played a dogged 5-4-1 formation in an effort to shut out his former club. They created little at the other end, but they drew level when Spanish forward Joselu headed in at the near post in the 83rd minute.
Chelsea got back in front with a fortuitous goal four minutes later from Yedlin, who had stretched his foot out to block a shot from Alonso which had looked to be going wide.
Chelsea join Liverpool and Watford at the top of the table on nine points after three games while Newcastle have one.
Hazard took the first of several painful knocks in the very first minute but remained a threat as Chelsea achieved almost 80 percent of possession in the first half and increased that figure in the second.
Newcastle, although pushed back, had one excellent chance before halftime when Salomon Rondon, on loan from West Bromwich Albion, headed wide.
He was replaced by Joselu after little more than quarter of an hour of the second half and after Chelsea also changed a striker, Olivier Giroud replacing Alvaro Morata, the game boiled up in the last 20 minutes.
Newcastle protested with some justification that Schar played the ball in his challenge on Alonso but Hazard nervelessly converted the penalty.
Chelsea were equally upset with the equaliser, claiming Giroud had been elbowed before Yedlin crossed for Joselu's fine header.
Then Yedlin became the fall-guy, deflecting Alonso's shot in for the winner.
"When they scored, I think everyone was thinking of a draw," Hazard said.
"But we are Chelsea, we never give up. We created a lot of chances and did very well today."
Newcastle manager Rafael Benitez felt his side were hard done by.
"The penalty was soft and changed everything as we had to be more open.
"We had five players out and thought if we were compact we could maybe frustrate them. We wanted to stay in the game and try to take our chances and we were very close."
Chelsea manager Maurizio Sarri was surprised that Newcastle played with five at the back.
"I have never seen a Rafa Benitez side play with five defenders," he said. "I think it is very difficult to play here for every team -- not only us. We were a bit unlucky when they scored to make it 1-1."
(Reporting by Richard Martin and Steve Tongue; Editing by Toby Davis and Christian Radnedge)
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