As on their previous trip to Merseyside before Christmas – a 6-2 rout of Everton– Mauricio Pochettino's side were in a clinical mood, although they had to wait until five minutes before half-time for Serge Aurier to spectacularly open the scoring.
The resistance Tranmere mustered before the interval dissipated afterwards as Spurs ran riot, with Llorente opening his account before Aurier completed an unlikely brace in the 55th minute.
Son Heung-min made it seven in his past six outings and two goals in as many minutes completed a treble for Llorente, whose replacement Harry Kane then got in on the act.
Tranmere goalkeeper Scott Davies made good early saves from Son and Lucas Moura but had no chance when Aurier dispossessed James Norwood and lashed home an unstoppable swerving strike from 25 yards.
Aurier was involved again as Tottenham doubled their lead three minutes into the second half. The former Paris Saint-Germain defender's clever flick sent Son into space down the right and his low cross was slotted in by Llorente.
Harvey Gilmour saw Aurier deflect his half-volley behind from Norwood's flick-on before the Spurs defender resumed activities in the Tranmere box, firing through Davies and the efforts of Mark Ellis on the line following a fabulous turn and lay-off from Son.
The South Korea star – who has delayed his arrival for duty at the Asian Cup – then glided towards and beyond a flagging Tranmere backline to clip home number four before the hour.
Tottenham were running through their full repertoire and Oliver Skipp's fine throughball allowed Llorente to peel away from Steve McNulty and finish in the 71st minute.
In the blink of an eye, the former Spain striker grabbed his third – stealing in front of Emmanuel Monthe to convert Lucas' cross.
Kane's introduction was hardly what Tranmere wanted and his unerring strike from Dele Alli's pass completed a comfortable outing for the Premier Leagueclub.
Spurs avoid a repeat of last season's FA Cup trails
Tottenham were forced into replays by Newport County and Rochdale in this competition last year but such struggles looked unlikely even before Aurier's spectacular opener.
Pochettino has made no secret of prioritising Premier League and Champions League commitments but Spurs' cup pedigree is becoming increasingly impressive. They were FA Cup semi-finalists in each of the past two seasons and face Chelsea at the same stage of the EFL Cup next.
Aurier returns with double delight
Since joining in August 2017, Aurier has not always convinced, while Kieran Trippier's superb development last season was something of a hindrance. However, having spent nearly a month on the sidelines with a groin injury, the Ivory Coast international relished meeting Tranmere's combative approach head on. If you see a better goal than his first during third-round weekend, you'll have witnessed an absolute stunner.
Rovers heavyweight McNulty left on the ropes
Tranmere captain McNulty is a cult hero with good reason – the defender's assured reading of the game and sure touch demonstrate his grounding as a member of Liverpool's academy setup. But errors and missteps peppered his display here, with Son and Lucas' livewire running proving too much to handle. 
