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.
In-form Tottenham Hotspur moved third following a 2-1 win at Sunderland where an apoplectic Gareth Bale was again booked for diving while fourth-bottom Aston Villa lost their third in a row in a 3-0 home defeat by Wigan Athletic.
Paul Lambert's Villa have conceded 15 in the three games and scored none.
Arsenal opened the scoring against leaky Newcastle through Walcott - again playing as a striker - when he escaped the offside trap and finished with aplomb in the style of boyhood hero and mentor Thierry Henry, who was watching from the stands.
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.
Ten-man Stoke City were facing a first home loss since February but a superb late Cameron Jerome strike secured a 3-3 draw with struggling Southampton and Reading pulled themselves away from last spot with a 1-0 home win over West Ham United.
Swansea City shrugged off the injury absence of top-scorer Michu to triumph 2-1 at Fulham where stand-in striker Danny Graham grabbed the opener.
CLEAN SHEET
Leaders United started with Van Persie on the bench and had Wayne Rooney out injured for a West Brom game that was nearly called off before kick-off because of heavy rain in Manchester.
Japan midfielder Shinji Kagawa made his comeback from injury but it was another returnee, winger Ashley Young, who provided the cross for McAuley to inadvertently score after nine minutes.
Ferguson's side have been consistently shipping goals, only prevailing 4-3 over New
