Following a goalless opening 40 minutes at Prenton Park, Serge Aurier started the rout with a deflected shot and doubled his personal tally in a nine-minute period that saw Spurs blow away their opponents with three goals early in the second half.
Having been taken to a replay in rounds four and five by Newport County and Rochdale respectively last season, Mauricio Pochettino named a fairly strong lineup that included Dele Alli, Lucas Moura and Son.
The Premier League side squandered two big opportunities in the early stages as in-form forward Son was kept out by the legs of Scott Davies and Lucas shot right at the Tranmere keeper.
Ben Davies was the next Tottenham player to test namesake Scott in the Tranmere goal, sending a well-struck shot down the middle, while Llorente volleyed a corner over the crossbar from 12 yards.
After being completely outplayed in the opening quarter of the match, Rovers soon grew into the contest and came close through a James Norwood shot into the side-netting and Manny Monthe's long-range header, which lacked the power to beat Paulo Gazzaniga.
Tottenham's goal therefore came somewhat against the run of play when it arrived five minutes before the interval, with Aurier's shot clipping Monthe and spinning away from Davies - his first goal for Spurs since netting against Bournemouth last March.
Any lingering hopes Tranmere had of pulling off an upset were killed off by a quickfire burst of Tottenham goals early in the second half.
Llorente tapped in from close range after being teed up by Son and Aurier fired home his side's third, finding a way through Davies and a covering defender on the line following a phenomenal touch from Son to play him in.
Not content with setting up a couple of goals, Son added his own name to the scoresheet by strolling past a couple of defenders and rolling the ball past Davies.
Substitute Oliver Banks and midfielder Harvey Gilmour both came close to pulling one back for Tranmere, but Tottenham turned it into a rout as Llorente bagged a second and third goal in the space of a minute.
The first was a smart finish past Davies following a fine through-ball from Oliver Skipp, while the second was a poked finish through the keeper, who could have done better to keep it out.
Alli blasted over the bar from a promising position as Tottenham, who brought on leading scorer Kane for Llorente with 15 minutes to go, closed in on a seventh.
That seventh goal arrived late on as Kane lifted the ball over Davies from an Alli assist to round off the scoring for a clinical Tottenham, who now host Chelsea and Manchester United over the next nine days.
TRANMERE ROVERS (3-5-2): Davies; Ellis, Monthe, McNulty; Caprice, Harris (Banks 58'), McCullough, Gilmour, Ridehalgh; Norwood, Jennings (Mullins 83')
TOTTENHAM HOTSPUR (3-4-3): Gazzaniga; Foyth, Sanchez (Eyoma 79'), Davies; Aurier, Skipp, Dele, Walker-Peters; Lucas, Llorente (Kane 75'), Son (Marsh 65')