Tottenham booked a fourth-round home clash with Southend after outclassing Cardiff in their FA Cup replay.
Spurs striker Robbie Keane celebrates his goal against Cardiff
Aaron Lennon broke the deadlock when he started and finished a swift break-out, with Robbie Keane soon doubling Spurs' lead from a Dimitar Berbatov pull-back.
Steed Malbranque, given too much time, picked his spot at the near post to give Spurs a 3-0 lead by half-time.
Cardiff rarely threatened and Jermain Defoe came off the bench to score Spurs' fourth after a blocked shot.
Keane, restored to the Spurs starting line-up after recovering fully from a knee injury, looked lively in combination with strike partner Berbatov.
Cardiff full-back Kerrea Gilbert, on loan from Arsenal, gave Keane's knee an early test by clattering the Republic of Ireland striker from behind.
In the opening exchanges at White Hart Lane the biggest threat to Cardiff goalkeeper Neil Alexander was his outfield team-mates carelessly giving possession away.
When Bluebirds youngster Joe Ledley committed such a sin after 10 minutes, Berbatov nearly exacted full punishment.
The Bulgarian international picked up the loose ball to burst between the startled Cardiff centre-backs, only to fire inches the wrong side of the post.
Another piece of sloppy Cardiff play, Kevin McNaughton's weak back-pass, nearly let Lennon sneak in.
Cardiff looked dangerous when they could deliver the ball into the Spurs area from set-pieces, but England keeper Paul Robinson was alive to the aerial threat.
Spurs goal-scorer Steed Malbranque is tackled by Cardiff's Kerrea Gilbert
His opposite number Alexander was still by far the busier and the Scottish international had to save smartly from Malbranque at point-blank range.
The pressure finally told after 27 minutes as the Premiership side launched a swift counter-attack.
Lennon picked up the ball deep in the Spurs half and scampered upfield before feeding Didier Zokora on the left.
When Zokora played a glorious pass back through the Cardiff area Keane was clearly in an offside position, but the ball rolled past the retreating Keane.
Lennon had continued his run and the England wing fired into the net as Cardiff waited in vain for an offside flag.
RATE PLAYERS: Tottenham v Leicester
606 DEBATE: Give your thoughts on the match
Cardiff's woe was doubled within three minutes, as Berbatov was allowed to slalom his way to the byline and cut the ball back for Keane to smash into the roof of the net from eight yards.
Alexander did well to palm away a Malbranque shot after being wrong-footed as it deflected off Cardiff skipper Darren Purse.
But Malbranque was not to be denied and just before half-time picked his spot from the edge of the area to shoot in at the near post.
Michael Chopra looked more lively after the break and promised to provide at least some goal-threat for Cardiff.
But the former Newcastle striker had a weak penalty appeal turned down by referee Mike Riley as he smartly turned Anthony Gardner.
Spurs were content to absorb what little threat their Championship guests could muster and look for opportunities to counter.
So it was no surprise when Defoe arrived off the bench for the last 20 minutes in place of Berbatov, adding his pace to the Spurs attack.
Defoe nearly played Keane in for Spurs' fourth, only for McNaughton's block to rescue things.
But Defoe soon added the coup de grace, following up to nudge home Hossam Ghaly's parried shot.
There was still time for Keane to draw one last save from Alexander as Spurs strutted their way to the final whistle.
The Londoners can now look forward to facing Southend in the fourth round, another off-form Championship side who Spurs defeated in the Carling Cup quarter-final last month.
Tottenham manager Martin Jol:
"I thought we bounced back well from disappointment at the weekend. We started well and we played some terrific football.
"We created a lot of chances and scored some really good goals.
"Steed Malbranque's work-rate is excellent and he can also score goals - he scored the best goal of the match."
Cardiff manager Dave Jones:
"For 20-odd minutes we've matched them in every department, but then we've gone to sleep and get caught on the break.
"We've had a three or four-minute mad spell where we've been our own worst enemies by giving the ball away.
"The second half was probably about damage limitation, but we've not really tested their goalkeeper."
Tottenham: Robinson, Chimbonda, Gardner, Dawson, Assou-Ekotto, Malbranque (Ghaly 65), Huddlestone, Zokora (Tainio 75), Lennon, Berbatov (Defoe 70), Keane.
Subs Not Used: Cerny, Young-Pyo Lee.
Goals: Lennon 27, Keane 30, Malbranque 41, Defoe 81.
Cardiff: Alexander, Gilbert, Purse, Loovens, McNaughton, Flood (Cooper 56), McPhail, Scimeca, Ledley, Chopra (Ferretti 75), Thompson.
Subs Not Used: Forde, Johnson, Campbell.
Ref: M Riley (W Yorkshire).