The 20-year-old midfielder opened the scoring on six minutes at Chelsea's Cobham Training Centre.
Callum Hudson-Odoi made it 1-1 with a wonderful solo goal on 21 minutes (see video below) but Ben Woodburn restored Liverpool's lead before half-time.
Wilson added his second on 71 minutes to maintain the six-point gap to second-placed Leicester City, who had beaten Derby County on Friday.
Chelsea drop to ninth.
Chelsea: 11 Dec v Derby (A) PL2
Liverpool: 28 Nov v Sparta Prague (H) PL Int Cup