Second-placed Tottenham's eighth successive league victory cut Chelsea's lead back to four points with five games to play after Antonio Conte's side had beaten Southampton 4-2 on Tuesday.
After Saturday's bitter FA Cup semi-final defeat by Chelsea, it looked like being a night of frustration for a labouring Spurs at Selhurst Park, especially after Dele Alli wasted a great chance to put them in front.
But they were eventually rewarded for a dominant second-half when Eriksen took aim from around 30 metres and beat Wayne Hennessey with a dipping low shot into the corner.
It was tough on Palace who lost defensive rock Mamadou Sakho early in the second half and looked exhausted late on after their excellent 2-1 victory at Liverpool on Sunday.
While Palace are all but safe from relegation, Tottenham can still dream of a first title since 1961 and now face a huge north London derby at home to Arsenal on Sunday.
"It is unbelievable. This is a tough place to come and we had to keep fighting. We knew our time would come and what a strike by Christian Eriksen," Tottenham striker Harry Kane said.
"We knew we had to bounce back after the weekend and what a performance by everyone. We knew we had to dig deep and get a goal. It was a perfect win in the end.
"We can't focus on Chelsea. We have five tough games. We have to win them to have a chance and hopefully we can do that."
Tottenham seemed to be suffering an FA Cup hangover in the early stages as a buoyant Palace, who had beaten Chelsea, Arsenal and Liverpool in recent weeks, gained the upper hand.
Tottenham were jittery and Christian Benteke should have done better when a good opportunity opened up but he shot too close to Spurs keeper Hugo Lloris.
Kyle Walker made a mess of Tottenham's first chance and Tottenham's unease increased when Victor Wanyama, who had already been booked, was lucky to avoid a second yellow card after a clumsy tackle on Andros Townsend.
Townsend drove another Palace effort over the bar as Tottenham struggled for fluency.
Wanyama and the hobbling Mousa Dembele were substituted at halftime with Spurs boss Mauricio Pochettio sending on Moussa Sissoko and Son Heung-min to inject some spark.
Palace retreated deeper after Sakho went off after appearing to catch his studs in the turf and Alli wasted Tottenham's best chance when he guided Walker's cross wide.
The hosts had 11 players behind the ball at times but could do nothing when Kane found Eriksen, and the Dane, impressive all night, sent the visiting fans into raptures.
(Reporting by Martyn Herman,; Editing by Neville Dalton)
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