Swansea took the lead through Premier League buy of the summer Michu on 37 minutes after a mistake by Branislav Ivanovic to set up the possibility of a first win at the Bridge in 87 years.
New signing Demba Ba was introduced with nine minutes left as Fernando Torres celebrated his 100th appearance for Chelsea with another toothless display. Ba was booked for diving in the 90th minute before the Swans quickly capitalised on yet another mistake by Ivanovic to sew up a two goal lead to take back to south Wales in the second leg.
Ba looked to have pulled a goal back in stoppage time but was ruled offside.
With Bradford pulling off a 3-1 win against Aston Villa, too, there is the very real possibility that the Capital One Cup’s showpiece final could be contested between the Yorkshire Championship side and Michael Laudrup’s impressive Premiership men.