Mauricio Pochettino's side had to be patient to make their bow at the Tottenham Hotspur Stadium after the estimated £1 billion ($A1.8 billion) project suffered a string of delays, but they immediately made themselves at home to end a five-game winless run in the league.
After a frustrating first half – which saw the Eagles comfortably keep the hosts at bay – Son Heung-min gave the home supporters something to cheer in the 55th minute, finding the bottom corner after a heavy deflection off Luka Milivojevic.
Christian Eriksen then added a deserved second 10 minutes from time as Spurs moved one point above Arsenal, who do have a game in hand over Pochettino's men.
Both sides enjoyed fine chances inside the opening 20 minutes. Jeffrey Schlupp blazed over after breaking the offside trap early on, while Eriksen's curled effort from 15 yards was well kept out by Vicente Guaita to his right.
The Palace goalkeeper almost gifted Spurs the lead nine minutes before the interval, though, when he fumbled Son's powerful drive just past the post.
Danny Rose then broke clean through but his attempted pass to Harry Kane was cut out, while the latter headed narrowly wide from a corner.
Michy Batshuayi flashed an effort wide of Hugo Lloris' left-hand post in the opening stages of the second period before Son netted his historic goal.
The South Korean cut inside from the right and unleashed a left-foot drive, which was diverted into the bottom corner by the outstretched leg of Milivojevic, who had been dispossessed earlier in the move.
Eriksen made sure of the points in the 80th minute, tucking home from six yards after a surging run from Kane to ensure Spurs christened their new home in style.
