City scored the first and last goals in a pulsating game, but Town netted three times in between and just about deserved their victory.
The game began edgily before Norwich had the first opening when ex-Town man Alan Lee played in Alan Gow, who dragged his angled shot wide.
City went in front on 16 minutes when Dave Mooney headed home Sammy Clingan's free-kick when left unmarked.
Town were level eight minutes later when Giovani Dos Santos' superb touch put Alan Quinn clear and he drove home from an angle.
Richard Wright tipped a fierce Darel Russell volley over before Santos almost picked out Pablo Counago right in front of goal.
Wright saved from Lee while Counago spurned a good chance at the end of the half, nodding over from substitute Jaime Peters' cross.
The second half began in even manner, David Marshall palming away a Santos shot and then Wright parrying away a fierce Gow drive.
Gary Doherty headed away a goal-bound Santos shot before Pim Balkestein and Veliche Shumulikoski shot over from good positions.
The home pressure told when Santos put Kevin Lisbie through and Marshall caught him to concede a penalty which Santos converted, although City protested Lisbie handled in the build-up.
Town were then happy to hit on the break as Norwich threw more bodies forward, but they created little to trouble Wright.
Marshall saved well after Doherty inadvertently deflected a David Norris cross towards his own net, before Wright had to be alert to deny substitute Cody McDonald after he collected a weak Ivan Campo back header.
Town looked to have sealed it in the final minute when substitute Jon Stead collected Wright's long punt and slotted coolly beyond Marshall.
There was still time for more drama as Quinn needlessly shoved Lee to concede a penalty which Clingan netted, but Town survived to take the derby honours.
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