In another bumper day for Premier League goals, resurgent Arsenal went fifth after a thrilling 7-3 home win over Newcastle United with contract rebel Theo Walcott scoring a hat-trick.
Manchester United maintained their seven-point advantage over City at the top after Gareth McAuley turned the ball into his own net and substitute Robin van Persie netted in a 2-0 win over West Bromwich Albion at a sodden Old Trafford.
"[Van Persie] changed the game for us," United boss Sir Alex Ferguson told the BBC. "When I brought him and Paul Scholes on they settled the game down for us. West Brom dominated in the second half and kept pumping the ball into our box.
"We're in a good position. We're halfway there."
City striker Dzeko scored twice in the first four minutes and another of his strikes was credited as an own goal by goalkeeper Mark Bunn at Norwich where Samir Nasri's 44th-minute red card had threatened the champions' dominance.
Paul Lambert's Villa have conceded 15 in the three games and scored none.
Demba Ba's deflected free-kick just before the interval gave the visitors hope but an excellent finish from Alex Oxlade-Chamberlain and a close-range header from Lukas Podolski after Sylvain Marveaux's leveller looked to have secured the points.
Ba then grabbed another equaliser but England's Walcott expertly found the top corner after 73 minutes and substitute Olivier Giroud bagged a double late on. A persistent Walcott then took the matchball to show he is not just a winger.
Ferguson's side have been consistently shipping goals, only prevailing 4-3 over New
