City's first league win in nearly a month put them on 46 points after 23 games, while the misery continued for Wolves, who are last in the table on eight points, 14 from safety. Arsenal can restore their seven-point cushion with a win over Manchester United on Sunday.

Starting ahead of Erling Haaland in his first league action since playing for Egypt at the Africa Cup of Nations, Marmoush put City on the scoresheet in the sixth minute with his first league goal of the season. Matheus Nunes, the target of boos from the travelling fans of his former team, swung in a cross from the right that Marmoush fired home.

"We fought until the end, showed a very good mentality from the beginning," Marmoush said. "(Guardiola) wanted us to put our hearts out there and fight for every ball.

"I am very happy to be here after AFCON and help my team. I saw that Matheus broke through and it was a good finish. Happy for the goal and happy for the three points. We just try to get our legs and mind fresh again and then we go again."

Semenyo, signed two weeks ago from Bournemouth, doubled City's lead in first-half injury time with his first league goal for the club, when Bernardo Silva found him on his right. Semenyo took a touch to set up his shot before unleashing a blistering low shot past goalkeeper Jose Sa.

The victory was City's first in the league since a 2-1 win over Nottingham Forest on December 27, with three draws and a derby loss to Manchester United since then costing them precious points in the title race.

Guardiola gave his league-leading scorer Haaland most of the afternoon off, after recently saying the Norwegian was "exhausted". Haaland, who came on in the 74th minute, has not scored in nine games.

Centre back Marc Guehi, signed earlier in the week from Crystal Palace, made an impressive City debut and had the Etihad Stadium crowd cheering when he blocked a Wolves shot to preserve the clean sheet.

“Really good," Guardiola said of Guehi. "With Marc, you see, the captain of Crystal Palace has to be something special. Really pleased for him. I know he’s so demanding and the demand for ourselves is to be better.”

City had four shots on target to Wolves' one, with Semenyo nearly doubling his tally when he latched on to a cross from Phil Foden late in the game but rattled his shot off the woodwork.

City also screamed for a penalty right before halftime for a close-range handball but after a lengthy VAR, the pitch-side review determined there was no penalty.

Wolverhampton's loss ended a run of positive results for the relegation-threatened side, with their previous defeat across all competitions coming on December 27 against Liverpool.

"It was a tough challenge, hard when you go 1-0 down so early on," Wolves boss Rob Edwards said. "The players did what we asked, we tried to be brave. We felt relatively comfortable, they didn't create too many moments.

"We pushed and we created some chances, we had a few shots but in the end we weren't able to break through. We kept them relatively quiet and really grew into the game well."

City host Galatasaray on Wednesday in a huge final league game of the Champions League. They are 11th in the table and need a top-eight finish to bypass the knockout playoff round.