Spurs handed starts to Kyle Naughton and Steven Caulker, with Kyle Walker and William Gallas dropping out, while the hosts drafted in Mladen Petric, Ashkan Dejagah and Kerim Frei for Damien Duff, Hugo Rodallega and Giorgos Karagounis.
The game got off to a slow start with both sides struggling to try and forge an opening, while Spurs had to replace skipper Michael Dawson after 16 minutes due to injury.
Midway through the first half Hugo Lloris made a fine save at his near post to deny Petric, while Spurs were unable to get leading scorer Jermain Defoe into the game.
Gareth Bale, who was earlier booked for diving, fired high and wide from the penalty spot to bring a drab first 45 minutes to a close.
Ten minutes into the second half Spurs made the breakthrough as Sandro picked the ball up 25 yards from goal and unleashed a swerving effort which beat Mark Schwarzer and crept into the net just inside the post.
The visitors doubled their lead 18 minutes from time as sub Gylfi Sigurdsson turned away from Philippe Senderos and set up Defoe, who finished calmly past Schwarzer.
The England man added his second and his side’s third five minutes later as he ran onto a through-ball from Clint Dempsey and again left Schwarzer well beaten.
Cardiff manager Neil Warnock labelled the postponing of his side's clash at Derby as 'scandalous' and a 'disgrace'.
Defender Russell Martin admits Rangers need to findways to win at Ibrox following their damaging 1-0 Ladbrokes Premiership defeat to Kilmarnock on Saturday.