Following the 2-2 draw in the initial third round fixture at St James' Park close to a fortnight ago, Jurgen Klopp's Reds made certain of their progress to the next phase with a commanding display at Anfield.
The opening goal came in the 10th minute when left-back Brad Smith played a neat one-two with Christian Benteke which allowed the Australian to cleverly cut back from the byline for Joe Allen to slot home with consummate ease.
The Reds had a host of chances to double their advantage during the first half but Benteke placed his pointblank header over the bar 10 minutes after the opener.
Cameron Brannagan and Jordon Ibe forced smart saves from Grecians gloveman Bobby Olejnik later in the half as Ibe's first Anfield continued to evade him when he fired into the crossbar early in the second lot of 45 minutes before the ball bounced down onto the goal-line but not fully over.
The Merseyside club finally grabbed a second through youngster Sheyi Ojo on 74 minutes to put the game further behind Exeter's reach.
The former Wolves loanee, who replaced Allen less than 10 minutes earlier, received a pass from Ibe on the right side of the area before producing a laconic curling effort beyond Oleynik and inside the far post to make it an Anfield debut to remember.
Liverpool then completely wrapped up proceedings on 82 minutes through Joao Carlos Teixeira who scored his first Liverpool goal when getting on the end of a nice through ball from Benteke to fire home from about 10 yards.
Klopp's side will now meet West Ham United at home in the fourth round to take place on January 30 as Exeter's run in the famous competition ends at the hands of a more superior outfit.
2015/16 FA CUP - THIRD ROUND REPLAY