James Ward-Prowse put the hosts in front in the 12th minute against the run of play. However, Antonio Conte's men fired back through Sessegnon and Dier to put them in front before the break.
Salisu then put the ball into his own net just after the hour mark and Kulusevski added a fourth goal two minutes later.
A bright start to the season for Tottenham, who play Chelsea next weekend (August 14) at Stamford Bridge in a crunch London derby.
Here are the main talking points from the match:
#5 Tottenham kick into gear after falling behind
Spurs fell behind against the run of play in the 12th minute but that moment served to spur them on as the hosts upped the ante and turned the match around.
With Sessegnon, Emerson Royal and Kulusevski offering great width down the flanks, Tottenham opened up the Saints.
Son Heung-min and Harry Kane ran between the lines to get to the end of the crosses from the wide players. Spurs enjoyed a period of sustained pressure after conceding.
It yielded great dividends as Sessegnon and Dier struck just 10 minutes apart to put Tottenham in front, following which there was no looking back for them.
#4 Kulusevski continues from where he left off last season
Dejan Kulusevski was one of the best January signings of last season in all of Europe's top five leagues. He registered five goals and eight assists in 18 top-flight matches after joining Spurs from Juventus.
On the opening day of the new season, the Swede has merely continued from where he left off, netting one fabulous goal and one stupendous assist.
He sent a brilliant inswinging cross for Sessegnon to head home from close as Spurs opened their account for the evening. He then netted their fourth goal with a confident finish from close range.
He won five duels and four tackles, won possession seven times, and had a passing accuracy of 92%. Since Kulusevski's debut for Spurs in February, only Ousmane Dembele (11) and Lionel Messi (10) have made more assists in Europe's top five leagues. The Swede has made nine assists.
Following a subdued period at Juventus, Kulusevski has recaptured his Parma form that brought him into the limelight since joining Tottenham. By the looks of it, he ain't stopping anytime soon.
#3 Salisu nets a bizarre own goal
The hosts' third goal was arguably the most bizarre moment of the game as Mohammed Salisu put the ball into his own net.
While attempting to clear Emerson's cut back, the Ghanian found himself in an awkward position near the line.
He tried to turn around before clearing the ball away. However, he couldn't quite position himself properly, and in a haste to clear the danger, accidentally sliced it home instead.
It added more wind to Spurs' sails as the hosts added a fourth goal just two minutes later.
#2 Sessegnon could become a key player for Spurs
Ryan Sessegnon had the world at his feet when he first joined Spurs from Fulham in 2019. However, it all went downhill from there for him when the Englishman failed to live up to expectations.
A loan spell away to Hoffenheim in the 2020-21 season couldn't help the forward revive his fortunes. He continued to struggle to establish himself in the first-team last season and wasn't helped by multiple injury issues.
He made just 15 Premier League appearances last season amidst injuries and competition from Sergio Reguilon.
However, the tides could be changing for Sessegnon this season. He was on target against Southampton, sneakily getting in behind the visitors' defense before nodding home from close range.
He scored another goal in the second half but was denied by the offside flag.
He remained a threat to the visitors throughout the game with his line-breaking runs and link-up plays. He was replaced at the 50-minute mark by new signing Ivan Perisic.
Overall, a very promising display.
#1 Tottenham made a huge opening day statement
Tottenham's 4-1 win today was their biggest ever on the opening day of a Premier League season, which could be a sign of things to come in the months ahead.
Antonio Conte's side played beautiful attacking football, giving Southampton no chance, at least after conceding the opening goal.
Spurs tore through the Saints with ruthless ease and created numerous chances as the north London side brought their A1 game.
If they can keep up this momentum over a sustained period, then Tottenham could be set for another top-four finish next May.