The defending champion has now lost three successive English Premier League games for the first time in 16 years, while manager Jose Mourinho has suffered seven league defeats in a season for the first time in his career.
The self-appointed "Special One" wasn't even present to see this latest setback -- he had to give the pre-match team talk from a hotel as he was serving a stadium ban for abusing officials following last month's loss to West Ham.
While some visiting fans wore Mourinho masks in support of the former Real Madrid, Inter Milan and Porto coach, the solidarity did not translate into an improved performance from his players.
Marko Arnautovic scored a spectacular scissor-kick in the 53rd minute to give Stoke a second home win over the London side in a fortnight, having triumphed after a penalty shootout in their League Cup clash.
The result moved Stoke up to 12th in the 20-team table and left Chelsea languishing in 16th -- 14 points behind the leaders.
Goalkeeper Asmir Begovic, signed from Stoke when Chelsea let Petr Cech join Arsenal, said the players were battling for Mourinho -- whose future seems less than certain despite receiving official backing from the club's board last month.
"We think he is the right man and someone we work hard for," the Bosnia and Herzegovina international told the BBC.
"His spirit and his presence is always there -- we wanted to get a result for him."
Costa, meanwhile, appears unlikely to face another ban, according to the UK Press Association, which reported that Stoke made an official complaint following the Spain striker's alleged incident with a steward.
Costa, suspended this season and last for on-field violent conduct, appeared to flick his leg backwards in the direction of a steward when he bent down to pick up a ball on the sidelines. PA later reported that the clubs had resolved the issue, though the matter would still be included in the referee's report.
While Costa seemed to score at will in the early stages of his debut Premier League season, his position as man of the moment has been usurped by an unlikely player in this campaign.
Jamie Vardy is now the first English player to score in nine successive league games -- one behind Dutch striker Ruud van Nistelrooy's all-time record for Manchester United.
Vardy's second-half winner for Leicester against Watford -- from the penalty spot after he was fouled -- was his 12th this season, giving him more goals than Chelsea has points (11).
Leicester, this season's surprise package under the guidance of former Chelsea coach Claudio Ranieri, joined Manchester City and Arsenal on 25 points at the top of the table after that 2-1 victory.
City, which qualified for the last 16 of the UEFA Champions League
in midweek, has the opportunity to go clear on Sunday with a match at bottom club Aston Villa.
Arsenal, whose European hopes hang by a thread after a 5-1 thumping at Bayern Munich
, next face the north London derby at home to sixth-placed Tottenham.
Unlike Chelsea, which beat Dynamo Kiev on Wednesday, Manchester United followed up its midweek Champions League success by winning 2-0 at home to West Brom.
Young midfielder Jesse Lindgard, who set up Wayne Rooney's winner against CSKA Moscow, opened the scoring with his first senior goal in the 52nd minute, while Juan Mata sealed victory at the end after Gareth McAuley was sent off for fouling Antony Martial.
United's seventh win in 12 league starts put Louis van Gaal's team one point behind the leading trio.