West Ham relieved the pressure on boss Manuel Pellegrini as they ended their seven-game winless run with a first victory at Chelsea for 17 years.
Aaron Cresswell scored the winner three minutes after the break as he cut inside and fired low past Kepa Arrizabalaga.
Chelsea had plenty of chances early on as Christian Pulisic missed the target from a few yards out. The American also wasted a great opportunity late on.
But Pellegrini was rewarded for picking 33-year-old David Martin in goal instead of Roberto as his side held firm under late pressure.
It proved an inspired choice as Martin, whose father Alvin is a West Ham legend, made several good saves to keep a clean sheet on his Hammers and Premier League debut.
The visitors also thought they had gone 2-0 up after 71 minutes, but Michail Antonio’s goal was ruled out for handball.
Victory lifted West Ham six points clear of the relegation zone while Chelsea failed to close the three-point gap to second-placed Manchester City and Leicester City in third.
However, the day belonged to Martin, who sank to his knees and was close to tears at the end of the game before celebrating in the stands with his father, who played in the West Ham defence for 20 years.
It was a performance, the elder Martin would have been proud of.
Emotional Martin helps engineer win
Third-choice keeper Martin came into the side after a woeful run of form by Roberto, who had shipped nine goals in his previous three Premier League games.
A lack of confidence in the Spaniard seemed to be affecting the team, who had not kept a clean sheet since their last Premier League win against Manchester United on 22 September.
Since then, the Hammers have slipped down the table, adding more pressure to Pellegrini, who according to some reports had two games to save his job prior to this victory.
But former Millwall and MK Dons keeper Martin seemed to lift his defence as the likes of Fabian Balbuena were in fine form.
Despite his age, the 33-year-old admitted afterwards he had struggled to eat once he knew he was set to play.
The nerves did not show, though, as he made a fantastic double stop to deny Mateo Kovacic and Oliver Giroud.
He was roundly cheered by the West Ham fans, who had booed Roberto during the 3-2 defeat by Tottenham last Saturday.
And his Hammers team-mates ran to congratulate him afterwards for a Premier League debut to remember.
Chelsea pay for profligacy
Although West Ham held firm, Chelsea paid for failing to take their chances with Pulisic perhaps the most guilty after lifting an effort over early on and slicing a chance wide after being put through by substitute N’Golo Kante.
To blame Pulisic, who has scored five goals in his last four Premier League games, would be unfair, though. He was among Chelsea’s best players as he attacked from the left, with Reece James also showing plenty of endeavour down the right.
Manager Frank Lampard, who had a stellar record against former team West Ham while playing for Chelsea, was missing top scorer Tammy Abraham, who injured his hip in the 2-2 draw at Valencia in the Champions League in midweek.
The Chelsea boss also made several changes as Kante started on the bench, and Mason Mount came back into the side where he battled against best friend Declan Rice in midfield.
But after the first 25 minutes where they were in the ascendancy, the game changed course after Arrizabalaga saved well from Antonio’s header.
The visitors grew in confidence from that chance and Chelsea struggled to contain their counter-attacks which eventually led to Cresswell’s goal.
Without the more mobile Abraham, Chelsea found their best chance came from the wings, but Giroud was poor and Mount was not clinical when he was presented with a sight of goal.
Willian came on to provide a boost towards the end, but Chelsea showed once again that when they cannot score, teams can find a soft core in their defence.
They have now conceded 20 goals in their 14 Premier League games, and following six successive wins, they have now suffered back-to-back defeats following last Saturday’s loss at Manchester City.
What next?
Chelsea host Aston Villa on Wednesday before travelling to Everton next Saturday. West Ham are at Wolves on Wednesday before hosting Arsenal the following Monday.
