Spurs celebrated the landmark victory in front of 59,215 boisterous supporters, who endured several delays before finally moving into the £1-billion Tottenham Hotspur Stadium.
Heung-Min Son's deflected effort in the 55th minute will go down as a piece of pub trivia. The tricky South Korean weaved through several defenders before unleashing a shot from the edge of the area and scoring the historic first goal.
Christian Eriksen secured the victory from close range in the 80th minute as Tottenham punished Palace on the counterattack.
"It's a special moment, a special night. I feel and believe it is the best stadium in the world," manager Mauricio Pochettino told Sky Sports.
The result snaps Tottenham's five-match winless streak in the Premier League and, more importantly, pushes them one point above crosstown rival Arsenal. The Gunners, however, still have a game in hand.