Dion Dublin and Darren Huckerby were both on target twice as Norwich cruised into the FA Cup fourth round.
Tamworth took charge early on, but Dublin headed Norwich in front six minutes before the interval and Huckerby swiftly slid home a second.
Keeper Jose Veiga blundered to allow Huckerby to add the third after 51 minutes and Dublin's clever finish punished more defensive uncertainty.
Kyle Storer's spectacular 68th-minute goal was no consolation for Tamworth.
Tamworth harboured hopes of a shock as they dominated early on, with John McGrath's shot from the edge of the area producing a scrambling save from Norwich keeper Paul Gallacher.
Steve Burton was also narrowly off target before Norwich's experience saw the Championship side take charge.
Robert Earnshaw had squandered a great chance when unmarked before Huckerby's cross into space at the near post was met by the diving Dublin six minutes before the interval.
And three minutes later the Canaries doubled their advantage, Dublin repaying the compliment by nodding into the path of Huckerby to steer a right-foot finish past Veiga.
Tamworth's hopes of a comeback were snuffed out after 51 minutes when Veiga allowed a tame shot from Huckerby to scramble under his body for Norwich's third.
Norwich were now in cruise control, and it was no surprise when Dublin added their fourth just after the hour, lofting a finish over Veiga after Tom Kemp missed an attempted clearance.
But Tamworth's endeavour was rewarded after 68 minutes when Storer fired a stunning right-foot drive beyond Gallacher into the far corner.
Tamworth manager Mark Cooper:
"During that time we were arguably on top and were creating chances but we didn't put any away.
"Against a good team like Norwich you will eventually be made to pay for that - as we saw.
Norwich striker Dion Dublin:
"But once we got a foothold in the match we settled and took control and it was a professional performance.
"In the end we had a little bit more quality than they did and we deserved to go through."
Tamworth: Veiga, Smith, Weaver, Kemp, Heslop (Law 89), Taylor, McGrath, Storer, Laight, Williams (Price 63), Burton (Atieno 56).
Subs Not Used: Mark Cooper, Dale Belford.
Booked: Weaver, McGrath.
Goals: Storer 68.
Norwich: Gallacher, Colin, Doherty, Shackell, Drury, Croft (Robinson 64), Safri (Hughes 69), Etuhu, Huckerby, Earnshaw, Dublin (Thorne 66).
Subs Not Used: McVeigh, Lewis.
Goals: Dublin 40, Huckerby 42, 51, Dublin 62.
Att: 3,165
Ref: P Walton (Northamptonshire).