The England midfielder struck after 56 minutes, finishing a flowing move with a firm goalbound shot from just inside the area that Watford defender Neil Cox could only head into his own net.
Liverpool, record seven-times League Cup winners, dominated the second half following the introduction of Czech striker Milan Baros as a substitute, wasting opportunities to extend their lead before the second leg at Vicarage Road in two weeks.
Watford, 16th in the second division, had competed well in the first half, threatening to open the scoring after 18 minutes when Brynjar Gunnarsson's powerful header was blocked by goalkeeper Jerzy Dudek.
Chelsea play Manchester United at Stamford Bridge in the first leg of the second semi-final on Wednesday. The final is at Cardiff's Millennium Stadium on February 27.
