City face replay, Stoke, West Ham advance
Bosnian striker Dzeko netted in the 80th minute to rescue City, who were left chasing the game after Neal Bishop headed the Magpies into a shock lead on 59 minutes at Meadow Lane.
City - who have spent more than £300m on players since their takeover by the Abu Dhabi United Group in 2008 - are currently 58 places above Notts County, languishing in 18th spot of League One. But the gulf between Roberto Mancini's expensively assembled squad and Paul Ince's side was rarely obvious as a quagmire of a pitch acted as a leveller.
In other fourth round matches, ten-man Arsenal needed a late Cesc Fabregas penalty to overcome Huddersfield Town 2-1 while Stoke City downed Wolverhampton Wanderers 1-0 to advance to the last 16 of the FA Cup.
In a thrilling encounter at Upton Park, West Ham United striker Victor Obinna scored a hat-trick as the Premier League side overcame Nottingham Forest 3-2 to advance to the last 16. Stoke meanwhile ended Wolves' FA Cup campaign after defender Robert Huth struck on 81 minutes at Molineux.
At the Emirates, second-half substitute Fabregas scored from the spot on 86 minutes after League One side Huddersfield had fought back bravely from 1-0 down to level in an open encounter. Fabregas's winner came after Terriers defender Jamie McCombe flattened Nicklas Bendtner in the area.
The Gunners, who had Sebastien Squillaci sent off just before half-time, had earlier taken the lead through a Peter Clarke own goal on 22 minutes. Huddersfield hit back through an Alan Lee header on 66 minutes to leave Arsenal facing the unwelcome prospect of a fourth round replay before Fabregas's late spot-kick saved the day.
Victory came at a cost for Arsenal however, with in-form midfielder Samir Nasri suffering a serious hamstring injury which could rule him out of his team's UEFA Champions League clash with Barcelona on February.