Israel international Hemed scored in the 51st minute, to move Brighton up four places to 13th, while ending the feel-good factor at Newcastle, who had been fourth ahead of the weekend's games.
Rafa Benitez's side, who drop down to joint eighth, had pipped Brighton to the Championship (second tier) title by one point on the final day of last season, having beaten them at home and away.
They had more of the game after bringing on midfielder Jonjo Shelvey, who hit a post direct from a corner, but good chances were hard to come by.
Both sides had lost their two opening games in the Premier League before an improvement gave them greater confidence at the higher level.
Brighton were the brighter side until the later stages once goalkeeper Mathew Ryan had saved from Mikel Merino early on.
They nevertheless had to survive the best chance of the first half, when a fortunate deflection off a home defender fell to Newcastle's Joselu.
Yet the Spanish striker, who was signed from Stoke City after a loan at Deportivo La Coruna, pulled his shot past the far post.
In an impressive spell at the start of the second half the home side went ahead and thought they had scored a second.
Dale Stephens was left unmarked at the far post to head a free kick square, from where Hemed hooked it in.
In almost the next attack Brighton captain Bruno crossed from the right for Solly March to squeeze in a shot that goalkeeper Rob Elliott blocked right on the line.
Once Shelvey replaced Isaac Hayden, Newcastle looked more threatening. He swerved a corner onto the post, then dipped a free kick just over the bar.
The visitors finished with more shots and more on target than the home side but still lacked the cutting edge necessary to push them back into the top four.
Newcastle manager Benitez felt there was a foul by Bruno in the build-up to the goal and that his team deserved "a point at least".
Brighton's Chris Hughton, celebrating a second successive home win, played down an incident in which Newcastle players suggested Hemed had stamped on DeAndre Yedlin.
"My first impression is no intent and knowing the individual I would say no intent," he told Sky Sports.
(Reporting by Steve Tongue; Editing by Toby Davis)
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