The Frenchman joined the Eagles on transfer deadline day from Celtic and made an immediate impact, coming off the bench to score twice in the final 10 minutes to put the game to bed.
After Japhet Tanganga had been earlier sent off for Spurs, Wilfried Zaha opened the scoring with a 76th-minute penalty as Palace won for the first time under Patrick Vieira.
Edouard, signed to end Palace’s goalscoring woes, needed just 28 seconds to score after his arrival before adding his second at the death.
“It’s a dream debut for me. I waited a long, long time for this and I’m very happy to score for the first win in front of the fans,” he told the club’s official website.
“I didn’t believe it… I need to enjoy it and for sure I’ll watch again my goals tonight. I’m very happy.
“(The manager) said, ‘Help the team, make a lot of runs behind. Try to help the team defensively and play like you do well’. So after I came on I wanted to score and help the team.
“It’s good I scored two goals and I’ll enjoy tonight, but tomorrow I go back to work.
“I want to work hard for next week and now this game is finished I want to forget and work hard for a good performance again.”
The defeat was Tottenham’s first of the season, after three previous 1-0 wins, and was perhaps no surprise after a difficult international period.
They lost star man Son Heung-min and attacking threat Steven Bergwijn to injury while Argentinian pair Cristian Romero and Giovani Lo Celso and Colombia’s Davinson Sanchez are in Croatia in order to avoid a hard quarantine following their decision to travel to South America for World Cup qualifiers last week.
Eric Dier picked up a serious looking knee injury 12 minutes in as Spurs’ plight went from bad to worse.
Spurs’ squad was stretched but boss Nuno Espirito Santo said there was no excuse.
“But this is what the squad is for. No kind of excuses,” he said.
“I believe that we have a good squad and enough quality and talent to overcome all the situations. What happened today and what happened during the week, it’s going to repeat all throughout the season so we’re going to have to be ready.
“The players have to be ready to step in and perform, and perform better and it’s my job to find the higher levels of performance that I believe our squad has.”
Nuno is hopeful that Son and Bergwijn might be fit for next weekend’s clash with Chelsea.
“Son doesn’t look well,” he added. “Stevie, let’s wait and see this week, but hopefully they will improve and be available for the game next week.”