And to make matters worse, key defender Micky van de Ven was sent off making him ineligible for their next Premier League clash against Liverpool.
Spurs started the night only one point outside the bottom three after West Ham won away to Fulham on Wednesday to make relegation to the Championship a serious possibility for the north-London club.
When Ismaila Sarr had a goal disallowed for offside and it was followed five minutes later by a 34th-minute opener for Dominic Solanke, Tottenham's luck appeared set to turn.
However, Van de Ven's inexplicable red-card for a blatant pull back on Sarr inside the area earned the stand-in home captain his marching orders.
Sarr tucked away the resulting spot-kick and scored again during a chaotic end to the first half in between Jorgen Strand Larsen's low effort.
Igor Tudor watched Spurs rally in the second half and not concede again, but this fifth consecutive defeat will leave the Croatian facing serious question marks over whether or not he is the right man to guide the 16th-placed club out of relegation trouble.
Tudor again rolled the dice for the visit of Palace with big-money signings Conor Gallagher and Xavi Simons dropped, but it failed to have the desired effect with Guglielmo Vicario forced to deny Adam Wharton inside 60 seconds.
Palace had the ball in the net just before the hour mark when Sarr raced onto Evann Guessand's through ball and finished well past Vicario, but a lengthy VAR check decided the attacker was offside.
Big cheers greeted the decision and moments later Tottenham seemed to have turned the tide when Solanke broke the deadlock and fired home in the 34th minute.
Four minutes later and Spurs' momentum was wiped out when Van de Ven pulled back Sarr to give away a penalty.
Referee Andrew Madley immediately pulled out a red card and after Sarr sent Vicario the wrong to score from 12 yards, Tottenham were left with a huge uphill task.
Tudor sent on Gallagher and Yves Bissouma, but shell-shocked Spurs conceded twice in first-half stoppage-time.
Wharton was the creator in chief for both, firstly threading a pass into Strand Larsen, who arrowed an effort past Vicario after he got away from Palhinha before Sarr grabbed his second.
Again, Wharton's clipped ball caught out Tottenham's static defence and Sarr poked in with Pedro Porro left to look foolish after he stood still with his hand up.
Loud boos greeted half-time, but despite the 10 men of Spurs rallying it couldn't prevent them from setting a new club record in the Premier League of 11 matches without a win.
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