Norwich cruised into the fourth round after scoring twice in each half during a classy display against Burnley.
Early headers by Grant Holt and Simeon Jackson made it 2-0 to Norwich before Jay Rodriguez pulled a goal back, nodding in a Ross Wallace free-kick.
Holt missed a penalty before the break after Charlie Austin was adjudged to have handled Andrew Crofts's cross.
But Andrew Surman's cool finish and Steve Morison's tap-in completed a well-deserved victory.
Norwich's Premier League quality shone through in their superior passing and movement. Wes Hoolahan was a major threat going forward for the Premier League side while Daniel Ayala impressed in defence.
Given how many of Norwich's players were in the Championship last season, the commanding nature of the victory illustrated just how far they have come in a short space of time under manager Paul Lambert.
It also demonstrated how much work Burnley have to do before a return to the top flight becomes realistic.
Lambert made five changes, including a rare start for Declan Rudd in goal, but their side was still strong as they faced a Burnley team who have made a habit of cup runs in recent years.
Burnley fielded three forwards - and came into the game on the back of three clean sheets in four matches - but any hopes of an upset were severely damaged by the quarter-hour mark.
Norwich's first came when Hoolahan showed his ability to deliver for Holt to head in. The Irishman then cut easily through Burnley again as he supplied Adam Drury, whose cross was met by a Jackson header that went in off the underside of the bar.
But Burnley's response was swift as Wallace's free-kick was finished by Rodriguez's impressive, looping effort.
The frantic start continued and Norwich threatened a third, as Crofts's strike from an awkward angle was blocked by Ben Mee, with the hosts' handball claims waved away by referee Mike Jones.
The home side were awarded a spot-kick when Crofts's cross was deemed to have been handled by Austin - it appeared a harsh decision - but Holt uncharacteristically failed to hit the target.
Rudd kept out Rodriguez's 25-yard volley then Ayala blocked a close-range Austin shot as Burnley failed in their attempts to force an equaliser before half-time.
Norwich pressed again early in the second period. During a goalmouth scramble, Hoolahan had a shot saved brilliantly by Grant, then Holt hit the post on the rebound, before Jackson somehow failed to steer in a follow-up from six yards.
But they restored their two-goal advantage after some neat build-up play that culminated in Drury's pass being flicked on delightfully by Jackson before Surman kept his composure to strike home.
Two Norwich substitutes made an immediate impact to put the result beyond doubt as their team strolled through the final stages of the match.
Aaron Wilbraham first forced a save from Grant, who could only push the ball into the path of Morison and the Wales international had an easy task tucking in the fourth.
Norwich manager Paul Lambert: "To go through is the most important thing, but we dominated the game from start to finish.
"Burnley have been doing well in the Championship but, hopefully, we have moved on from last year when we had two really tough games against them.
"The Premier League does that to teams, with the level and the intensity you play at. It makes everybody step up to the plate and it was important nobody went below that."
Burnley manager Eddie Howe: "Norwich have definitely improved and got some good players with consistent results. As such, they are hard to beat.
"We were not at full strength today and, when you come to a Premier League ground, you need to have your best team with you to have any chance.
"We will learn from it and hopefully have a good second half to the season."