Michail Antonio’s 22nd-minute opener in south London was followed up by a Manuel Lanzini first-half brace to move the Hammers within a point of fourth-placed Arsenal.
After winning in seven of their opening 11 league games, West Ham have struggled for consistency in recent months but survived late goals by Odsonne Edouard and Michael Olise to back up Tuesday’s 4-1 thrashing of Watford with another three points to remain in fifth position.
“This time of the year you take what you get, you are churning the players out, trying to get them ready for games when you don’t know how they will be, so I have to praise the players,” Moyes said.
“I’m thrilled with us getting these results. I have told the players we set really big standards at the start of the season and we need to get back to them.
“We’re trying to get back to them and there has been small signs of us getting better.
“Our goalscoring is coming back after we went a few games away from home without scoring, so we’re scoring away which is pleasing me but we need to get back to being pretty mean and not allowing teams opportunities to get back in games.”
After a slow start at Selhurst Park, a tap-in from Antonio after a wonderful Said Benrahma cross put West Ham ahead before they doubled their advantage in the 25th minute.
Declan Rice carried the ball forward impressively in midfield and found Lanzini, who showed superb close control to get away from Joachim Andersen and rifle into the roof of the net. The Argentinian added another from the penalty spot in first-half stoppage-time to make it four league goals for the season.
Moyes added: “Lanzini has played well for us at the moment and we’ve needed him to give us something slightly different while we’ve maybe not got the same rhythm as we had for the opening three or four months.
“He is chipping in, helping us with his play and helping us with his goals as well.”
Palace boss Patrick Vieira returned to the touchline after missing the last two games with Covid-19 and was frustrated they were unable to convert their chances.
Jeffrey Schlupp hit the post early on while Edouard hit the crossbar and squandered several openings before he pulled one back from Olise’s cross with the provider then turning goalscorer in the 90th minute when his free-kick evaded everyone to find the net.
“I think when you concede the first goal, the way we manage the next 10 to 15 minutes, this is a lack of experience,” Vieira insisted.
“We are building something here which will take time but the first half shows some parts of the game we need to improve.
“Overall, we give West Ham a really good game and this is something we have to be pleased about because they have been working together for the last couple of years, building the team and the way we play them away and at home gives us a lot of hope for the future.”
Vieira conceded referee Darren England was right to award a penalty at the end of the first half after captain Luka Milivojevic handled but would not be drawn on his heated conversation with the official at full-time which resulted in the Palace manager being booked.
He added: “I just expressed myself. I get the yellow card that I accept and there is nothing more to say.”