A week on from their hard-fought 1-0 triumph at Liverpool, the Eagles blew the Hammers away on home soil and raced into a three-goal lead inside the opening 20 minutes, the earliest they have ever lead by a 3-0 scoreline in Premier League history.
Star winger Olise put Oliver Glasner's men ahead in the seventh minute with a close-range header after meeting a delightful ball from Joachim Andersen, who found himself in an unfamiliar left-wing position following a corner.
An exquisite acrobatic effort from Eberechi Eze doubled the hosts' advantage shortly before Emerson Palmieri prodded Will Hughes's cross into his own net.
Olise then turned provider for fellow attacker Jean-Philippe Mateta, flashing the ball across the face of goal for the Eagles striker to slide home a fourth from close range just after the half-hour mark.
Olise makes Premier League history in five-star Palace display
Mateta added his second and Palace's fifth midway through the second half, in between a strike from Michail Antonio and a late own goal from Dean Henderson, and Glasner's men eventually celebrated back-to-back Premier League wins for the first time this season.
Olise, who has been linked with a host of top Premier League clubs including Manchester United, Manchester City, Arsenal and Chelsea ahead of the summer transfer window, was one of the standout performers for Palace, and his two goal contributions have seen him set a new Premier League record.
Indeed, at the age of 22 years and 131 days old, Olise is the youngest player to have been directly involved in 10 or more goals in each of the last two Premier League seasons.
The France Under-21 international contributed with two goals and 11 assists in 37 Premier League games in the 2022-23 campaign and has since chipped in with seven goals and four assists in 14 top-flight matches during an injury-hit 2023-24 season.
Glasner: 'Palace were a joy to watch'
Glasner was delighted with his side's performances and believes it was the best way to follow up last weekend's triumph at Liverpool.
Speaking to cpfc.com, the Austrian said: "Are we still hungry, are we still ambitious after this big win at Anfield? Because very often, maybe the concentration, the focus goes down a little bit.
"You think about many situations that can happen in a game, with injuries or you have a red card down, so maybe you can change things. But I had no plan in my head when we were four goals up after 30 minutes!
"That's the best situation you can have, and I really enjoyed today watching the players, what kind of joy they had in possession, how they combined, and it was really amazing to watch them.
"You could feel it in the whole of Selhurst Park, the fans were happy, the players were happy, and that's how football should be. But it's also important to keep this focus high over 95 minutes.
"The players, how they started the game in the first 30 minutes, were really amazing. It was nice to watch for a manager. It was an excellent performance, but now the game is played. The game is played, the three points we have, and it's the first back-to-back wins of the season.
"Now it's the third one in a row against Newcastle [we are aiming for], and this will be a big challenge (next Wednesday)."
Palace sit 14th in the Premier League table and have all but secured their top-flight status for another season as they sit 11 points clear of the relegation zone and have a game in hand on 18th-placed Luton Town.