Frederic Kanoute grabbed a hat-trick as Tottenham eased into the fourth round. The striker coolly sidefooted his first following a Gus Poyet pass and tapped in his second after a dazzling run by Stephane Dalmat.
Johnnie Jackson and Robbie Keane went close before Kanoute sealed victory shortly after the break from Ledley King's pass.
Guy Poyet was sent off for allegedly spitting while Palace's Danny Butterfield saw red for a late lunge.
Tottenham, looking for their first win in five matches, welcomed skipper Stephen Carr back to their starting line-up, while Welsh winger Simon Davies was on the bench after four months out with a hip injury.
Palace included Cedric Berthelin in goal in place of on-loan Thomas Myhre, who was refused permission to play by Sunderland.
And the French keeper was busy right from the outset as Spurs dominated.
Kanoute twice almost gave the home side the lead, with Berthelin saving at his near post and the Spurs man then narrowly fail to turn in Jackson's rasping low drive.
 | KEY MOMENTS 14 mins: Kanoute opens the scoring 20 mins: Kanoute taps in his second 48 mins: Kanoute seals his hat-trick 78mins: Poyet sent off 82mins: Butterfield sent off |
But the impressive Kanoute deservedly gave Spurs the lead on 14 minutes when he coolly side-footed home after a fine run and deft flicked pass from Poyet.
Palace had both Ben Watson and Michael Hughes cautioned in the opening quarter of an hour as they tried in vain to keep pace with their Premiership opponents and they soon found themselves trailing 2-0.
The livewire Dalmat was the creator, dancing through three challenges before crossing from the right for Kanoute to tap in from six yards.
Wayne Routledge and Andrew Johnson looked Palace's best chance of getting back into the match but they lacked support and Tottenham should have wrapped up the win by half-time.
Jackson was denied by the on-rushing Berthelin after another superb Poyet pass and Kanoute and Dalmat also went close.
Any hopes of an unlikely Palace revival were killed off three minutes after the break when Kanoute latched onto King's clever scooped pass and calmly finished.
Keane should have made it four a minute later but blazed wildly over when one-on-one. Butterfield, substitute Dougie Freedman and Michael Hughes all had shots easily saved by Kasey Keller late on but by this time Spurs were coasting home.
The only late excitement came as tempers flared in the final 10 minutes with both sides reduced to 10 men.
First Poyet saw red for allegedly spitting after a late challenge by Freedman and three minutes later, Butterfield got his marching orders for a lunging tackle on Spurs substitute Bobby Zamora.
Tottenham: Keller, Carr, Taricco, Doherty, Gardner, Poyet, Dalmat, Jackson (Zamora 73), King (Davies 62), Keane, Kanoute.
Subs Not Used: Hirschfeld, Postiga, Kelly.
Sent Off: Poyet (79).
Booked: Jackson, Doherty.
Crystal Palace: Berthelin, Butterfield, Symons (Smith 69), Popovic, Borrowdale (Granville 80), Routledge, Watson, Hughes, Gray, Shipperley, Johnson (Freedman 45).
Subs Not Used: Black, Fleming.
Sent Off: Butterfield (82).
Booked: Watson, Hughes, Freedman.
Attendance: 32,340.
Referee: A D'Urso (Essex).