- Nicolas Jackson (50')
Pressure had been mounting on new Chelsea manager Mauricio Pochettino after a poor start to the season that has seen them win just one of their first six games in the Premier League.
Scoring has been a major issue with just five goals in those six league games, but summer signing Jackson provided a reason for optimism for the Chelsea fans with a clinical first-time finish in the 50th minute. The former Villarreal forward was set up by Cole Palmer, who was making his first start for Chelsea after joining from Manchester City.
Jackson thought he had doubled his and Chelsea's tally in the 72nd minute but the goal was ruled out for offside.
Despite that, a Chelsea team featuring three players -- Marc Cucurella, Robert Sánchez and Moisés Caicedo -- who were signed from Brighton did enough to hold on for a much-needed first win in September.
Earlier on Wednesday, Chelsea defender Reece James was charged by the English Football Association for an alleged altercation with a match official.
James has been given until Friday to respond to the charge.
The England international did not play in the game at Stamford Bridge because of injury.
- Thomas Bramall