Hayden Hackney scored the only goal on 38 minutes as the Championship side held out against Mauricio Pochettino's expensively assembled array of underperforming stars. A fifth defeat in six away games heaps more pressure on Pochettino, with Chelsea languishing in 10th in the Premier League.
The Blues must turn the tie around when the sides meet again at Stamford Bridge on January 23 to avoid the latest embarrassment in a disappointing first season in charge for the Argentine.
Despite the club spending over £1 billion on players in the last three transfer windows, Pochettino suggested last month he would need to look to strengthen once more in order to address the lack of a goal threat. Noni Madueke looked the most likely spark to Chelsea's attack, but he was sacrificed as Pochettino threw on Mykhailo Mudryk and Armando Broja.