Former Arsenal midfielder Vieira had seen his side take just one point from their opening three Premier League games, but Wilfried Zaha's 76th-minute penalty and a debut double for new signing Edouard in the final 10 minutes earned 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.
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 arrived at Selhurst Park as the only team with a 100 per cent record from their opening three games but the international break did not treat them kindly.
Son Heung-min was one of three players to pick up an 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 some World Cup qualifiers last week.
It left the visitors with a skeleton of the team that had begun the season so well and they struggled to impose themselves on the game as Palace dominated proceedings.
Zaha was proving to be a menace on the left and was at the heart of everything Palace did well.
He had two efforts in quick succession, which were both deflected wide, and then created Palace's best moment of the first half.
The Ivorian beat Emerson Royal and Pierre-Emile Hojbjerg and pulled the ball back for Conor Gallagher, but his low shot from close range was kept out by goalkeeper Lloris.
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.
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.