Bukayo Saka struck twice, while Leandro Trossard and centre-backs William Saliba and Gabriel Magalhaes were also on target in a ruthless display from Mikel Arteta's men as they set a new club record for a Premier League away win.
Victory takes the Gunners back to within two points of Premier League leaders Liverpool and behind Manchester City only on goals scored.
"We were 4-0 up in the first half and we could have scored more," said Saka.
"We smelled blood today and went for the kill."
The wheels of Arsenal's challenge for a first league title in 20 years appeared to be coming off when they lost at home to the Hammers amid a run of one win in seven games either side of the new year.
However, they have bounced back emphatically since a two-week winter break to lay down the gauntlet to perennial title challengers City and Liverpool at the top of the table.
“I felt that the team had the right desire, straight after Liverpool, because it was something still in their tummy about what happened with West Ham at the Emirates and we wanted to put it right," said Arteta.
"If you want to be at the top, we're going to have to be really consistent and play at that level, and we certainly did it today."
West Ham had beaten the Gunners twice this season, also dumping them out of the League Cup in November.
But they were outclassed to up the scrutiny on Moyes, who is out of contract at the end of the season.
"They started the game brilliantly from minute one, let's not kid ourselves, it wasn't just those (four goals) 15 minutes," said Moyes.
"I'm not used to my team conceding the goals like we have been."
Saka makes amends
Arsenal's title challenge last season began to wobble when they blew a 2-0 lead at the London Stadium last season.
This time there was never any doubt of the outcome once Saliba headed home Rice's corner to open the floodgates on 32 minutes.
Saka missed a penalty in that draw last April, but made no mistake from the spot after he had been brought down by Alphonse Areola.
Rice led West Ham to Europa Conference League glory in his final game for the club before moving to north London for a fee in excess of £100 million.
The England international was given a clear demonstration of why he had to make the move to fulfil his ambition of more silverware as another wicked Rice delivery was nodded in by Gabriel.
Trossard pilled on the West Ham pain in first-half stoppage time as he cut inside to fire brilliantly into the top corner.
That goal was the trigger for many of the home support to leave for the afternoon as the second half was played out in front of vast swathes of empty seats.
Arsenal added two more goals in two minutes just after the hour mark.
Saka's first had been his 50th Arsenal goal and he cut inside to fire home in trademark fashion on his left foot.
Rice then rubbed salt in West Ham wounds with a stunning finish into the top corner from outside the box.
The midfielder refused to celebrate out of respect for his former teammates and supporters.
But after Arsenal were criticised by some members of the media for going overboard in their celebrations of a 3-1 win over Liverpool last weekend, there was even more for Arteta and his players to get excited about.
