Edouard scored the fastest goal by a Premier League substitute, scoring just 28 seconds after being introduced.
The home side had taken the lead through the impressive Wilfried Zaha,.
Zaha cooly slotted home from the penalty spot after Ben Davies had handled Conor Gallagher’s attempted cross.
Former Arsenal midfielder Vieira had seen his side take just one point from their opening three Premier League games, but a debut double for new signing Edouard in the final 10 minutes secured a deserved three points.
Vieira was part of the Gunners team that dominated north London for the best part of a decade and he will have enjoyed ending Spurs’ 100 per cent start to the season with a dominant display.
Edouard’s second in stoppage time concluded a disastrous afternoon for Spurs.
Nuno Espirito Santo’s side were under-strength and off the pace in south London and there was no coming back after Japhet Tanganga was sent off just before the hour after picking up two yellow cards in the space of five minutes.
Spurs registered their first shot on goal shortly after the second half began as Lucas Moura tested Vicente Guaita’s handling from distance before a real flashpoint at the other end.
With Palace on a quick break, Tanganga cynically wiped out Zaha and the pair immediately clashed, sparking a huge melee.
They were both booked, with Zaha perhaps lucky to escape a red card after appearing to grab his opponent by the face.
Instead it was Tanganga who walked five minutes later after lunging tackle on Jordan Ayew earned him a second yellow card.
That decision gave the hosts further control and they probed for an opener. But in the end they were given a helping hand in breaking the deadlock.
Conor Gallagher’s cross hit the outstretched arm of Ben Davies and the linesman immediately flagged, with Zaha sending Lloris the wrong way from the spot.
Edouard, a deadline day signing from Celtic, settled the game with his first touch after coming off the bench.
Zaha caused more damage down the left and his cross was swept home by the Frenchman.
It soon turned into a great afternoon for Edouard as he made it 3-0 at the end, converting after Gallagher had played him in.
Additional reporting by PA
Tottenham player ratings vs Crystal Palace
Dan Kilpatrick has had his say on how each Tottenham player fared on a difficult afternoon in South London:
Next up for Crystal Palace…
Patrick Vieira is up and away as Crystal Palace manager – was there ever any doubt the former Arsenal midfielder would get his first win against Tottenham? Their next fixture is another tough one, with a visit to Anfield on the cards next Saturday. That was a performance to boost their confidence; Conor Gallagher looks a really good signing.
A damning verdict from the Evening Standard’s chief football correspondent
Tottenham left with more questions
That was a disaster of an afternoon for Nuno Espirito Santo. Tottenham looked terrible, with Harry Kane completely out of the game and the rest of the attack struggling without the injured Heung-min Son. Eric Dier’s injury causes further defensive problems, and Tottenham play twice next week. Their Europa Conference League opener with Rennes on Thursday is followed by the small matter of another London derby with Chelsea. It could be another tricky week.
Wilfried Zaha and Odsonne Edouard speak to BT Sport
“That felt special,” says Zaha. “We have been working on trying to play football and today we showed it. I am happy I managed to take a penalty today and score one for the team.
“We continued playing we have been. The chances will come and we have just got to take them. I can’t say training is enjoyable but the results are showing.”
“I am very happy with my debut,” adds Edouard. To score in front of the fans is very beautiful for me and the team. It was my dream. I worked very hard for this moment.”
Full Time: Crystal Palace 3-0 Tottenham Hotspur
Patrick Vieira’s Crystal Palace have ended Tottenham’s unbeaten run. It’s a 3-0 defeat for Nuno Espirito Santo’s side and one they thoroughly deserved, second best even before the sending off of Japhet Tanganga in the second half. A disastrous week for Spurs continues, with Tanganga now suspended and Nuno likely to be without Eric Dier for an extended period after the centre half limped off in the first half.
FULL TIME: CRYSTAL PALACE 3-0 TOTTENHAM HOTSPUR
GOAL! CRYSTAL PALACE 3-0 Tottenham (Odsonne Edouard, 90+ 3 minutes)
And it is three! Edouard again!
Tottenham have thrown men forward in their bid for an unlikely turnaround and Crystal Palace break beautifully, play switched delightfully to Michael Olise, who slips the ball inside to Conor Gallagher.
Gallagher draws and passes to Odsonne Edouard in space, and despite a healthy hand from Hugo Lloris the Frenchman cannot prevent his compatriot doubling his debut tally.
90 + 2 minutes
Lucas Moura gestures like a crazed puppeteer as he and Harry Kane miscommunicate down the right. Kane really hasn’t been in this.
Crystal Palace win back possession and break…
Emerson Royal vs Wilfried Zaha has been a thoroughly entertaining individual duel. Royal has coped reasonably well at times on debut and shows an impressive turn of speed to get back to Zaha after he appeared to have been beaten as we move into three minutes of stoppage time.