Son Heung-min and Lucas Moura missed good chances to extend Spurs' lead before halftime as a nervous energy began to take hold of the home crowd.
Cardiff created chances and came close to equalising in the second half when Josh Murphy raced through and lifted the ball over Spurs goalkeeper Hugo Lloris, making his first Premier League start since August. However, defender Toby Alderweireld was able to clear off the line.
Neil Warnock's side, looking for their first win of the season, were reduced to 10 men in the 57th minute when Joe Ralls was sent off for a cynical lunge on the lightning-quick Moura.
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They still threatened, with Lloris tipping a Sean Morrison header on to the post from a floated free kick.
Spurs failed to take advantage of the extra man, perhaps still looking a bit shell-shocked from their 4-2 defeat by a Lionel Messi-inspired Barcelona in the Champions League on Wednesday.
But they saw out their third successive league victory which took them to third in the standings, within a point of leaders Manchester City who face second-place Liverpool on Sunday.
"After Barcelona on Wednesday, the most important thing was to win," Spurs manager Mauricio Pochettino said. "I think we fully deserved to win, we created a lot of chances, (but) we didn't kill the game.
"But I am happy to finish and to go into the international break with 18 points, one point to the top is fantastic. Of course, we can always improve."
At the other end of the table, the situation looks bleak for Cardiff who only have two points from eight games.
Manager Warnock was pleased with his team's performance but was frustrated with the sending-off, and accused Tottenham's players of influencing the referee's decision.
"I thought Mike Dean, experienced referee, was going to give a yellow card right from the start... I'll be very surprised when I speak to him if he would've given the red card (without influence), because I think he was wrong. He was wrong," Warnock told Sky Sports.
"But when 20 players surround you, all wearing a white shirt, all big name players, I think it influences them (referees) at times and it would be interesting to see if he reports that."
(Reporting by Christian Radnedge; Editing by Pritha Sarkar and Ed Osmond)
