The England goalkeeper, who endured a mixed 2018-19 campaign, blocked efforts from Jordan Ayew and then Max Meyer as Palace put the visitors under pressure in the second half.
German Meyer also went close in the first half when his goalbound effort looped behind off the foot of Seamus Coleman.
- All the Premier League action
- Relive the action from Selhurst Park
- Premier League 2019-20: BBC Sport pundits pick champions and top four
- VAR should not kill game – Milivojevic
Marco Silva’s Everton dominated much of the first period with Gylfi Sigurdsson firing a yard wide before full-back Coleman smacked a shot into the body of goalkeeper Vicente Guaita.
Sigurdsson produced another effort that was blocked on the line and team-mate Richarlison curled a sumptuous effort narrowly wide of Guaita’s upright.
Palace’s Wilfried Zaha, who handed in a transfer request and was the subject of a summer window bid from the opponents, came on in the 65th minute to warm applause.
He failed to affect the scoreline as did the 76th minute sending off of Morgan Schneiderlin, who picked up a second yellow for a foul on Luka Milivojevic, as Everton kept Roy Hodgson’s men at bay in the closing stages.
Pickford comes to Everton’s rescue
It was a 2018-19 season of contrasts for Pickford. He entered it as England’s number one after his World Cup heroics and exited it with some questioning whether he deserved to retain his spot.
The former Sunderland keeper made four errors that led to goals in the league last campaign and that count does not include a farcical rugby tackle on Newcastle’s Salomon Rondon which resulted in a penalty much to the delight of the St James’ Park support.
He could ill-afford more of those lapses of concentration in the opening game at Selhurst Park. Instead he produced an outstanding display, making himself big to deny Ayew and Meyer.
He also remained alert with seconds remaining as Connor Wickham came charging in at the near post in attempt to convert Zaha’s near-post delivery.
Cheers greet Zaha
Both sides must have WIShed they had a Zaha operating at 100%. Everton, who had a bid of £52m for the winger turned down in the transfer window, could have done with his guile and pace to open up the Palace defence in the second half.
As for the Eagles, they held on to a player who provided 10 goals and five assists last season but then told the club he wanted to leave.
Hodgson suggested in the build-up that the winger was not in the right frame of mind, so it came as no surprise he did not start. When he was finally introduced, with 25 minutes to go, would he be greeted with cheers or jeers from the home support? It was largely the former.
He made little impact on the match in the short time, bar one piece of play when he fed the ball to Patrick van Aanholt who almost found Christian Benteke at the far post.
If Hodgson can get Zaha’s mind right then it could be another positive season for Palace.
Man of the match – Jordan Pickford (Everton)
‘He’s such a natural phenomenon’ – reaction
Palace manager Roy Hodgson speaking about Zaha on BBC’s Match of the Day: “He did quite well, he did what we hoped he would do – create opportunities, put Max Meyer in one v one, a couple of times he had to be bundled off the ball at the last minute.
“Of course, when you’ve been away for three weeks, he’s such a natural phenomenon as an athlete but to get him back to full capacity will take him a week or two.”
Everton boss Marco Silva: “It was a tough game, competitive as you would expect. We lost Andre Gomes [to injury in the first half], we were controlling the game, creating moments – it’s clear for me in some moments when you bring in new players they need time to adapt.
“Today was a good example, we lost some balls in zones we cannot.
“Our first half deserved something more. A clean sheet, the attitude was there. We lost some easy balls and if they didn’t happen we would have controlled the game until the end.”
Schneiderlin joins select club – the stats
- Everton have drawn their opening game in six of the last seven Premier League campaigns. However, this is the first time they’ve began with a goalless draw since 1998-99.
- Since the start of last season, Palace have failed to score in more league home games than any other current Premier League side (nine).
- Only Manchester City (13) have kept more Premier League clean sheets so far in 2019 than Everton (11).
- The last shot on target in this match came after 62 minutes, from Sigurdsson.
- Schneiderlin became the third Everton player to be sent off on the opening weekend of a Premier League campaign, after Li Tie in 2003-04 and Phil Jagielka in 2018-19.
- Schneiderlin’s sending off made Everton the first team to receive a red card in consecutive Premier League opening weekends since Arsenal in 2010-11 and 2011-12.
- 3van Aanholt
- 4MilivojevicBooked at 55mins
- 7MeyerBooked at 38mins
- 17BentekeSubstituted forWickhamat 83′minutes
- 9J AyewSubstituted forZahaat 65′minutes
- 18SchneiderlinBooked at 76mins
- 21André GomesSubstituted forGbaminat 45+1′minutes
- 10G SigurdssonSubstituted forDaviesat 79′minutes
- 20BernardBooked at 52mins
- 9Calvert-LewinSubstituted forKeanat 69′minutes
- Jonathan Moss
Delay over. They are ready to continue.