Mauricio Pochettino's side failed to score for the second consecutive Premier League game and were indebted to goalkeeper Hugo Lloris for helping secure a draw
Spurs were looking to win back-to-back home games in the Premier League for the first time this season, but failed to break down a resolute Palace backline.
While Neil Warnock's side had the better of the first half in north London, largely inspired by lively wingers Yannick Bolasie and Wilfried Zaha, Palace had their defensive ranks to thank after the break.
The visitors did well to keep the likes Harry Kane and Roberto Soldado quiet in the face of almost constant Spurs possession as Warnock's men bounced back from their 1-0 defeat at fellow strugglers Aston Villa on Tuesday.
|VIEW FROM WHITE HART LANE
|By Greg Stobart
It tells the story that the biggest cheer of the game came when the big screens here erroneously reported that Arsenal were 4-0 down at Stoke.
Tottenham may have avoided a defeat like their bitter rivals but that did not stop the supporters from expressing their opinion with loud boos at the full-time whistle. The hosts were outplayed by Palace throughout the afternoon and when they created their one real chance, Roberto Soldado sliced horribly wide.
The visitors will be disappointed that they were denied twice by Hugo Lloris, once by the crossbar and once by a linesman’s flag as they played with too much intensity for their hosts.
The Spaniard in particular spurned his fair share of chances, displaying a lack of sharpness despite scoring his first league goal since March against Everton last weekend.
Both sides had chances late on - substitute Jason Puncheon almost giving Palace their first away league win since September when he rattled the crossbar - as sections of the home support voiced their discontent at the goalless draw.
Christian Eriksen sparked the game into life following a relatively low-key start, as he cleverly nutmegged Martin Kelly before firing into the side-netting seven minutes in.
Palace's first sight of goal came shortly after as James McArthur blazed high and wide it was Bolasie's turn to showcase his skills.
Bolasie beat Eriksen with a deft spin before setting up the returning Joe Ledley to fire over after 20 minutes.
With Palace on top, Soldado - one of two Spurs changes - missed the opportunity to put the hosts in front against the run of play when he cleared the crossbar from inside the area.
Jan Vertonghen - making his 100th Tottenham appearance - was needed to deny Zaha's progress soon after following a tricky run into the area.
Having switched wings with Bolasie midway through the half, Zaha went close again prior to the interval as the Manchester United loanee bamboozled Eric Dier and Ryan Mason before curling his strike wide.
Mauricio Pochettino brought on Nacer Chadli for Erik Lamela at the break, but Spurs continued to be contained by a well-drilled Palace outfit.
The home side dominated possession and upped the pressure in search of an opener, with Soldado slicing a shot well wide from inside the area following an incisive ball from Eriksen just after the hour.
Palace almost grabbed the winner 17 minutes from time as substitute Puncheon crashed a strike off the underside off the crossbar before Joel Ward blocked Paulinho's goalbound strike inside the six-yard box.
However, the spoils were shared in a result that will likely please Warnock much more than his opposite number Pochettino.