Chris Palmer's early strike gave Gillingham hope but the Canaries showed their quality, ensuring an early cup exit for the Gills at a half-empty Carrow Road.
Andy Hessenthaler's team lined-up in a 4-4-2 formation, with Andy Barcham partnering Akinfenwa in attack. Luke Rooney took up the advanced role in a compact midfield diamond, with Jack Payne pulling the strings in front of the back four.
Norwich took just five minutes to strike the Gills woodwork, Chris Martin, firing a free-kick against Alan Julian's left-hand upright, despite having been booked moments earlier for attempting to take his set-piece too quickly.
Then, after barely escaping their own half in the opening ten minutes, The Gills promptly took the lead. John Nutter's throw-on was touched into the path of Barcham, his progress was blocked on the edge of the box but Chris Palmer pounced on the loose ball, driving a low left-foot shot beyond Ruddy and into the far corner.
With the Canaries visibly subdued, Gillingham really should have been 2-0 up on 23 minutes as Adebayo Akinfenwa rose unmarked from six yards out to head Danny Spiller's left-wing free-kick onto the cross bar. Unfortunately Bayo's effort came back off the underside and was cleared to safety before the Gills could force in the rebound.
Three minutes later, Gillingham were left to rue that missed opportunity as Chris Martin levelled the scores. Grant Holt's intelligent dink over the back four sent Martin clear and, as Bentley slid in to tackle, the City forward swept his finish into the net.
Soon after, Simon Lappin's corner carried to Wes Hoolahan, who flashed wide with a shot across goal from the left of the box as Norwich regained their momentum. Sure enough, a second goal followed on 31 minutes, as Gillingham were undone by a lovely flowing move that saw Korey Smith send Russell Martin away down the right, Grant Holt heading his centre beyond a helpless Julian.
Six minutes before the interval, Norwich hit the woodwork for a second time after Rooney had fouled Lappin on the edge of the box. Chris Martin took responsibility and thwacked the crossbar with a rising drive that ballooned to safety off the top side of the bar.
Moments later, at the opposite end, Jack Payne made space in the box to shoot but saw his effort palmed away by Canaries custodian John Ruddy. Akinfenwa was on hand, lurking with intent at the far post but headed wide with the goal at his mercy. That proved to be Payne's last contribution as the youngster limped off with what looked like a dead leg, to be replaced by Kevin Maher.
HT 1-2
Both sides made a bright start to the second half, though it was Norwich once again who enjoyed the better of the early action.
Inevitably, Grant Holt was able to extend City's advantage in the 55th minute after good link-up play between Hoolahan and Smith on the right of goal. The latter curled a neat ball to the near post and Holt shrugged off the attentions of Mark Bentley to hook in a simple finish from close range.
Doubtless the Gills back four were grateful to see the back of Holt who was subbed midway through the half. His departure triggered an encouraging spell for the visitors who drew a save from Ruddy on 66 minutes. Palmer's cross was held up by Akinfenwa, who laid off to Luke Rooney but the Canaries keeper stood up well to block his rising effort from the just inside the area.
On 79 minutes Alan Julian was called into action to push Chris Martin's powerful free-kick to safety after referee Andy D'Urso incorrectly ruled that Kevin Maher had fouled Hoolahan on the edge of the box.
With seven minutes of normal time remaining Andy Hessenthaler handed young striker Andy White his senior debut. The former Reading apprentice replacing a tiring Bayo Akinfenwa. Seconds later ,Tony Sinclair picked up the Gills first booking of the night for clumsily restraining Chris Martin en route to goal, fortunately McNamee thumped the resulting free-kick over Julian's crossbar.
In the closing stages Martin forced his way into the box once more, but shot tamely into the arms of Julian before Norwich claimed a fourth in time added-on. Oli Johnson eased past Gowling to win a ball over the top, his touch sent Martin clear, who in turn rounded Julian to complete a comfortable win for the Canaries.
Attendance: 13,068
Gillingham: Alan Julian, Tony Sinclair, Josh Gowling, Mark Bentley, John Nutter, Jack Payne (Kevin Maher 42), Danny Spiller, Chris Palmer, Andy Barcham, Adebayo Akinfenwa (Andy White 83), Luke Rooney (Stefan Payne 71)
Subs not used: Lance Cronin, Danny Jackman, Connor Essam.
Norwich City: John Ruddy, Russell Martin, Adam Drury, Michael Nelson, Grant Holt (Oli Johnson 64), Wes Hoolahan (Anthony McNamee 79), David Fox (Mathew Gill 69), Chris Martin, Korey Smith, Simon Lappin, Elliott Ward
Subs not used: Declan Rudd, Stephen Hughes, George Francomb, Jens Berthel Askou.

















