The highlight in front of a noisy, near-full Stamford Bridge was when academy product Trevoh Chalobah smashed home their third from 25 yards on his Premier League debut.
Blues boss Thomas Tuchel said before the game he was surprised his side – who are European champions and won the Uefa Super Cup on Wednesday – were considered among the favourites to win the title.
But they were excellent in their league opener as Vieira’s first game as a manager in England resulted in a limp performance.
Marcos Alonso whipped in Chelsea’s opener with a free-kick from about 22 yards.
Christian Pulisic then blasted in a second via the underside of the bar after Vicente Guaita spilled Mason Mount’s cross.
And Chalobah, who joined Chelsea’s youth set-up 14 years ago, drove home from distance to seal the win.
Palace improved slightly after the break, but Jordan Ayew’s header was their only effort on target.
No Lukaku, Kante, Ziyech, Chilwell, Havertz, no problem
Chelsea’s remarkable squad depth is why many people expect them to win the title this season.
Seven of 20 BBC pundits tipped the Blues, with the other 13 going for champions Manchester City.
Striker Romelu Lukaku was not able to play because he is still quarantining after his £97.5m move from Inter Milan. Influential midfielder N’Golo Kante and winger Hakim Ziyech were injured against Villarreal on Wednesday.
England left-back Ben Chilwell, experienced centre-back Thiago Silva and Kai Havertz, who scored the winner in the Champions League final, were left on the bench.
Ex-Blues midfielder Joe Cole said during the week that every decision Tuchel makes seems to pay off.
And it felt that way when Alonso, who started instead of Chilwell at left wing-back, curled in a perfect free-kick to give them a deserved lead. Palace offered so little threat that he basically played as an orthodox winger.
Pulisic then continued his fine form against Palace with a close-range finish after Guaita spilled a cross. Five of the American’s 13 Premier League goals have come against the Eagles.
They had plenty of chances to score more with Timo Werner’s first touch letting him down on a couple of occasions and Alonso forcing a good save from Guaita.
But the best moment of the game came when 22-year-old Chalobah, who made his Chelsea debut in Belfast three days ago, picked the ball up in space and drilled home via the inside of the post.
There were plenty of cheers too when Champions League hero Havertz came on – the first time he, or many of this Blues squad, have played at a full Stamford Bridge.
Vieira should forget this and move on
This was the first Palace game under legendary former Arsenal midfielder Vieira, who previously managed New York City in the USA and Nice in France’s Ligue 1.
He warned beforehand that “to put my ideas in place may take longer”, but this was as hard a first game as he could have anticipated.
Nine first-team players left the club over the summer – mostly at the end of their contracts – after manager Roy Hodgson’s exit. Despite that, only one summer signing started – £18m defender Marc Guehi, against the club that sold him this summer.
Joachim Andersen, who was relegated with Fulham last season, came on in the second half.
Palace are hoping to have a more youthful look after the departure of those ageing players – and 18-year-old winger Jesurun Rak-Sakyi made his debut from the bench.
Vieira’s side – who started with a four-man defence and also tried a back five – failed to have a single shot or touch in Chelsea’s box in the first half. They had to wait an hour to test Edouard Mendy but even then Ayew’s header was straight at the Blues keeper.
Jeffrey Schlupp fired over and Christian Benteke shot wide but there was never a single moment in the game when the Eagles looked like scoring.
Their next game – against promoted Brentford next Saturday – is the real acid test of how Vieira and Palace are looking.