A Ben White own goal put the home side in front before strikes from Mohammed Kudus and Jarrod Bowen early in the second period put the tie beyond doubt.
Arsenal have signed England international Declan Rice on a long-term contract from West Ham United, the north London club said on Saturday.
Liverpool boss Jurgen Klopp said on Tuesday he has taken pleasure in West Ham's revival under David Moyes as it prevented him from becoming the oldest manager in the Premier League.
The draw meant Chelsea have now won only one of their last seven league games - and they have not won away since October. They stayed ninth in the table, nine points behind fourth-placed Newcastle who have played a game less.
Chelsea are looking to win their first away game in the league since October, a run of six matches which included three losses at Potter's former club Brighton & Hove Albion, Newcastle United and Fulham.
West Ham have appoint former Everton and Manchester United boss David Moyes as their new manager.
Premier League strugglers West Ham United come back from two goals down to beat Tottenham Hotspur 3-2 at Wembley Stadium.
West Ham United captain Mark Noble is to undergo surgery for a long-standing abdominal injury and will miss the last two Premier League games of the season, the club said on Thursday.
West Ham United manager Slaven Bilic has called on his players to drop their egos and work as one in order to end their woeful run of five consecutive Premier League defeats when they host relegation-threatened Swansea City on Saturday.