The victory is Spurs’ biggest win away from home in the club’s 136-year history.
The seven-goal mauling was also Tottenham’s largest margin of victory since they beat Wigan Athletic 9-1 in 2009, and the club’s biggest FA Cup win since they overcame Crewe 13-2 in a fourth-round replay 59 years ago.
Surprisingly, Spurs took 40 minutes to break the deadlock at Prenton Park, which came through through Serge Aurier, who also bagged his second 10 minutes after the interval. It was the former PSG man’s first ever career brace.
Aurier’s double also means he scored more goals on Friday than he had during his previous 35 appearances combined.
Fernando Llorente also was on the scoresheet for Tottenham, and the Spanish striker netted a hat-trick for Pochettino’s side.
Llorente has now scored three in each of his last two starts in the FA Cup. The 33-year-old recorded a hat-trick when Spurs beat Rochdale 6-1 last February.
Son Heung-min was the third player to get on the scoresheet for Tottenham before he was replaced on 65 minutes. Harry Kane added a seventh and final goal in the 82nd minute - his ninth in the last eight FA Cup matches.
The win means the north London club are the first side to qualify for the fourth round of the cup and will hope their Premier League rivals slip up during the remainder of the weekend's fixtures.
Kane and Son were among a number of first-team players selected for Tottenham, as well as Ben Davies, Dele Alli and Lucas Moura, who played all 90 minutes.
Tottenham have not won a major trophy since claiming the League Cup in 2008, and is often levelled as an argument against Pochettino’s success at Spurs.
Next up for Tottenham is the Carabao Cup semi-final first leg against Chelsea which will take place on Tuesday at Wembley Stadium.
That is followed by a weekend Premier League clash with Manchester United, also in London. A win could help reduce the deficit to leaders Liverpool who, following the results from the Premier League's midweek matches, Spurs trail by six points.