Scott Rogers' charges gave a good account of themselves, but the Londoners carried more clinical threat in the final third.
In bitterly cold conditions, the tie at Prescot Cables FC went ahead following a morning pitch inspection.
Rogers was still without the services of influential captain Gemma Bonner while loanee and leading scorer Bethany England couldn't play against her parent club.
Liverpool started brightly with Laura Coombs and Caroline Weir seeing plenty of the ball in midfield. A superb pass from the latter almost put Martha Harris through on goal, but she was blocked out well by the covering Millie Bright.
Chelsea were dangerous in wide areas, though, and they took the lead via Jonna Anderson in the 21st minute. A driving run from Romana Bachmann found Drew Spence down the left, and her low cross was drilled into the net by Anderson.
The home side responded well. Weir let fly from 25 yards only to see Carly Telford react well to smother the ball at the near post.
A smart free-kick from Kate Longhurst on 38 minutes caused panic in the Chelsea rearguard, but neither Coombs nor Weir could get any meaningful contact as the away side scrambled the ball away to safety.
And Chelsea then made it 2-0 two minutes before the break when Katie Chapman met a free-kick to send a header beyond the reach of Siobhan Chamberlain.
The visitors made it three on 57 minutes via a penalty. Alex Greenwood brought down former Red Gemma Davison and Maren Mjelde stepped up and made no mistake with her spot-kick.
Liverpool: Chamberlain, Murray, Harris, Greenwood, Rodgers, Ingle, Longhurst, Coombs, Clarke (Johnson), Weir, Hodson.
Subs not used: Flaherty, Babajide, Roberts.