Palace created the better opportunities but after a fine showing by stand-in goalkeeper Paulo Gazzaniga, Son Heung-min's second-half strike proved to be the difference between the sides with a 1-0 scoreline being recorded for the fifth time in six meetings.
The result sees third-place Spurs move back level on points with Manchester United, while Palace remain rooted to the bottom of the standings as they extended their run without an away goal in the top flight to 736 minutes.
Spurs started the game tentatively but it was Harry Kane who got the first shot on goal in the 10th minute, with a sharp turn being followed up with a 30-yard volley which went straight into the gloves of Julian Speroni.
The home team would have expected to build on that opening, but Palace's defensive work - and numerous stoppages in play - ensured that Spurs would have to wait until the half-hour mark for their next chance, with Danny Rose heading wide at the back post.
Kane also headed over from inside the penalty area, but Palace almost took a surprise lead with 10 minutes of the first half remaining when Scott Dann rose above Eric Dier at a corner, only to see Gazzaniga pull off an excellent one-handed save down to his left.
The let-off was a wake-up call for Spurs but Palace had little trouble in reaching the break still on level terms, with Mauricio Pochettino's men looking devoid of ideas in the final third.
Mousa Dembele was introduced at half time but three minutes after the restart, it was Palace who threatened again through Andros Townsend, with the former Spurs man outpacing Dier before seeing a low shot tipped wide by Gazzaniga.
Spurs were seeing cross after cross blocked by the Palace defence, and the Eagles should have capitalised before the hour mark after creating two more opportunities.
Townsend's through-ball to Wilfried Zaha sent the winger clear of the defence but after rounding Gazzaniga, Palace's star man missed an open goal from 18 yards.
Moments later, Luka Milivojevic's header at the back post was blocked by the goalkeeper as Palace threatened to end their long run without a goal on their travels, but it would be Spurs who would break the deadlock in the 64th minute.
The Palace backline made two more blocks inside the penalty area but the ball fell to Son on the edge of the box, with the attacker curling a shot into the corner from 20 yards out.
Despite falling behind, it was Palace who continued to have the better of the game, although shots from Zaha and Cabaye were never really threatening an equaliser.
However, as the game moved closer to a conclusion, Roy Hodgson began to throw more men forward and that resulted in his team losing their previous balance, giving Spurs more room to try to score a second.
It should have arrived through Son after being played through on goal by Jan Vertonghen, but the forward tried to be too clever and dragged a shot into the side-netting from 10 yards out.
The closing stages passed by without incident, but that suited Spurs as the North Londoners comfortably saw out their final fixture between the international break.