The Carabao Cup holders trailed inside seven minutes at the Etihad Stadium as Marmoush completed a quick one-two but despite Dan Burn's sliding tackle inside the box, the ball bounced kindly off the Egyptian forward before looping over Magpies goalkeeper Aaron Ramsdale.
Joe Willock, on target in last week's 1-1 draw against Paris Saint-Germain in the UEFA Champions League, missed an opportunity to draw United level in swift fashion. After Anthony Gordon made a positive run in behind the City defence before squaring the ball into Willock's path, the midfielder attempted to round James Trafford but the City goalkeeper quickly dived at his feet to claim the ball.
Gordon went close to netting his 11th goal of the season across all competitions. After Ramsdale's goal kick was headed towards goal by Burn and Willock, the latter's flick on found Gordon but the left winger's low first time effort was blocked out for a corner by a sprawling Trafford.
Newcastle conceded a second goal in the 29th minute as Marmoush doubled his and City's lead. After Tijani Reijnders completed a lengthy run before finding Antoine Semenyo, the Ghanian's low pass across the face of goal was hooked into the air by Kieran Trippier before Marmoush rose high inside the six-yard area to nod the ball into an empty net.
United suffered a further blow as Reijnders scored three minutes later, beginning a dangerous attack from distance and after Semenyo initially checked inside, the former was on hand in the box to place the ball beyond Ramsdale.
The visitors' frustrating evening continued as Gordon was withdrawn in the latter stages of the first half due to a hamstring issue.
Howe made a triple substitution before the restart, with Jacob Murphy, Elanga and Yoane Wissa all introduced and the latter went close to scoring United's first goal at the Etihad Stadium since DeAndre Yedlin's strike in a 2-1 loss back in September 2018.
After latching onto Sandro Tonali's pass, the Congolese striker raced towards goal but sliced a wild effort wide of the target.
Newcastle pulled a goal back, though, as Elanga - who joined United from Nottingham Forest last summer -netted his first goal for the club in the 61st minute, driving into the box from the right flank before firing a fierce effort into the far corner via the left-hand post.
Newcastle United: Aaron Ramsdale, Kieran Trippier (c), Lewis Hall (Jacob Murphy 46), Sven Botman, Sandro Tonali, Anthony Gordon (Harvey Barnes 43), Malick Thiaw, Nick Woltemade (Yoane Wissa 46), Joe Willock (Anthony Elanga 46), Dan Burn, Jacob Ramsey.
Substitutes: Nick Pope, Will Osula, Alex Murphy, Leo Shahar, Sean Neave.
