Hull broke the deadlock on 21 minutes with a superb strike from on-loan Manchester United youngster Robbie Brady.
Doni was beaten for a second time 13 minutes later when Robert Koren found the net after working a one-two with Aaron McLean.
Henderson and Downing were among those introduced for the second half as Kenny Dalglish made 11 changes, and Downing went close to scoring within two minutes when his effort was superbly saved by Hull keeper Adriano Basso.
Hull added a third just before the hour when Jay Simpson scored from close-range to condemn Liverpool to their first defeat of pre-season.
Source: Team Talk
Source: Team Talk