Marmoush marked his Man City debut with a goal in the 19th minute, expertly lobbing Martin Dubravka after receiving a long pass from his goalkeeper, Ederson.
The Egyptian forward was in scintillating form, netting a first-half hat-trick to effectively seal the game.
James McAtee added a fourth goal late on, making it another punishing day for Newcastle at the Etihad. The Magpies haven’t won an away game at City since 2000 and now find themselves three places and three points behind City in the Premier League standings.
Erling Haaland, who captained City to victory, was forced off with a knee issue late in the match, raising concerns for Guardiola ahead of their crucial Champions League clash against Real Madrid.
Guardiola will at least be happy with his side’s performance and singled out two “extraordinary” performances.
“The way we played, we remembered what we were and what we have not been this season,” he said.
“We always try, but sometimes we cannot do it. I am really pleased with the pace and intensity we had up front, Nico (Gonzalez) and (Abdukodir) Khusanov were extraordinary.
“We need to win these games to qualify for the Champions League. We have to make this kind of performance to send our people home happy.
“Marmoush did really well in Germany, a player with his quality and pace, I was pleased with the way he scored. Against Orient he missed chances, but today in the final third he was really good.
“Haaland has signed a 10 year contract, so I have the feeling about him as captain. I am really happy for him.
“Sooner or later (he will be long-term captain). A question of time.”
Marmoush was in a thankful mood after scoring a hat-trick, which he never managed in the Bundesliga with Eintracht Frankfurt or Wolfsburg.
“Amazing day, the feeling is crazy,” the Egyptian said. “And the three points, we came in from the first minute and got the job done. It was all fast paced, I was really happy to help the team.
“I also have to thank my team-mates, the coach and staff, everyone helped me from the first day making me feel part of this family.
“It was an amazing atmosphere, I would like to thank the fans for the really nice applause.”
Newcastle head coach Eddie Howe, meanwhile, said he believes a trip to Man City is still the “toughest” match in the Premier League despite their struggles this term.
“It was a tough game, they are still the toughest team to play against,” he said. “We were not at our best today.
“Goals change games, and the goal we concede early was a tough one for us. All the goals we conceded today we will look back on with frustration. It becomes difficult when you chase the game today, really tough.
“They ask so many questions of you, put you under pressure. They did not have a bundle of chances but they did what they needed to do.
“It’s about growing for the next games and learning from today. When you come back into these arenas, fare better, that’s the challenge.”
Howe added: “It was a tough day at the office – they played well, we didn’t. The goals were poor moments, we will have to analyse them and work out what we could do better.
“From the off we were lacking in duels, the physical side. Man City are so good in the build-up, to disrupt that you have to be exceptional physically and we weren’t.
“We can’t look for excuses, there are a load of reasons we could look at, but the players should have been fresh and ready to perform, they didn’t.
“We’ve got some tough games, the fixture list will test us. We have to dust ourselves off for next week.”
