The England worldwide overtook Shearer's 22-year record for Premier League goals in a calendar year, while also usurping Messi as Europe's top scorer for club and country in 2017.
The England worldwide, who has made history in just 36 appearances compared to Shearer's 42 for Blackburn in 1995, put Spurs into a two-goal half-time lead with a close-range header and a simple tap-in before completing his second successive hat-trick with a dinked finish over Saints goalkeeper Fraser Forster for his side's fifth.
Speaking of Messi, his 25th Clásico goal over the weekend in Barcelona's 0-3 win at the Santiago Bernabéu against Real Madrid saw him move onto 54 goals for club and country this year.
Tottenham have collected 13 points from their last five Premier League games to hoist themselves up to fifth place in the table. At the season's halfway mark, Kane's 15 goals have him leading the Golden Boot standings, level with Liverpool's Mohamed Salah. He now has eight hat-tricks in total over the 12-month period.
The footballer said he was delighted to be compared to Lionel Messi and Cristiano Ronaldo.
"First of all I want to congratulate Harry Kane, a massive achievement for him, well deserved", the Argentine coach said after the game.
Dele Alli and Son Heung-min each struck to make it 4-0 to Spurs, while Saints pulled goals back through Sofiane Boufal and substitute Dusan Tadic. "To get another hat-trick is a great way to end the year".
Spurs have been the Premier League's best team over Christmas in each of the last two seasons - winning seven straight matches from December 14 a year ago - and their back-to-back title challenges have been built on formidable second halves to the season.
Harry Kane was sensational as Tottenham's front four dominated Southampton for a big Boxing Day win.
"I think he deserves everything", Spurs boss Mauricio Pochettino said.
Saints visit Manchester United on December 30 and barring a shock, they're likely to start 2018 in the relegation zone or just above it.
Alli then turned provider as Spurs quickly broke from Nathan Redmond's mistake on the edge of Spurs' area, Alli strode forward before playing the through ball for Son on the right-hand side of the area and made no mistake as he fired it low into the opposite corner.