With manager Manuel Pellegrini absent after returning to Chile due to a family issue, City, beaten 2-0 by Supersport United in their opening friendly, fell behind when Bongani Ndulula made the most of Aleksandar Kolarov’s mistake to put the home side ahead.
England midfielder James Milner pulled the visitors level with a fine cross-shot, only for Nyadombo to score from the spot in the final seconds.
There was better news for City off the pitch as Italian club Fiorentina confirmed that Montenegro striker Stevan Jovetic is set to join the Premier League club.
City are also close to the signing of Sevilla striker Alvaro Negredo and their need for new attackers was once again demonstrated in Durban, with Samir Nasri and Edin Dzeko failing to form a dangerous partnership.
City midfielder Gareth Barry felt that the team’s fitness had let them down against Supersport United in Pretoria on Sunday.
The English outfit began with far greater intensity this time and were unlucky not to take the lead when a dipping free-kick from Nasri was pushed just past the post by AmaZulu goalkeeper Kapini Tapuwa.
But in the 20th minute at the Moses Mabhida Stadium, City gifted the home side the lead with some poor defending.
Kolarov’s poorly struck pass gave Matija Nastasic no chance and after Ndulula beat goalkeeper Joe Hart to the ball he was left with an easy finish into an empty net.
City replied five minutes later with an impressive finish from Milner.
Scott Sinclair found space down the left flank and sent over a cross that was met with a weak connection by Yaya Toure but Milner made sure with a firm drive across goal.
Milner was involved again just before the hour when his low cross was missed by Dzeko.
Micah Richards also went close with a header from a deep corner from Nasri shortly before half-time.
City employed different teams in each half of the Supersport match but just three changes were made at the interval this time, with Argentina defender Pablo Zabaleta, allowed to return to training late after international commitments, given his first taste of action.
The visitors almost pulled ahead when Dzeko’s cross-shot was pushed away by goalkeeper Aubrey Mathib.
Sinclair also dragged a shot wide and Denis Suarez missed with a header from Joleon Lescott’s cross as City pressed for a second goal.
But Abdul Razak was penalised for pulling Marc van Heerden over in the area and Nyadomo scored from the spot.