In attack Kane was a constant menace and scored his 200th career goal with a composed finish following a slick exchange of passes with Alli, albeit the England captain appeared to be marginally offside when he struck.
Redmond fired into the side-netting from an acute angle, while Pierre-Emile Hojbjerg nearly found the top corner of Lloris net with a shot from 15 yards out.
In a message to Tottenham fans, chairman Daniel Levy said: "We are delighted that we shall be able to welcome our supporters to the stadium and our players of the past and the future to take to the pitch on what will be momentous occasions for our Club".
"I'm going to tell what I told before: I am a little bit anxious [about] this change".
While the goals for the Saints didn't come until the end of the second period, there was more vigour and energy from Ralph Hasenhuttl's side, who are still in a battle to avoid relegation from the Premier League, with a moment of magic from Ward-Prowse deciding the contest.
Canada sees second straight monthly employment surge with 55,900 net new jobs
Youth aged 15 to 24 drove employment growth for the second consecutive month, accounting for more than half of total job gains. The report says the addition last month of 67,400 full-time jobs more than offset a loss of 11,600 part-time positions.
"The following has been agreed with the Premier League, Brighton and Crystal Palace to ensure that our first game is a Premier League match prior to a UEFA Champions League quarter-final match", a Tottenham statement said.
"It is about competing better for the first goal if you want to be a contender for big things".
Tottenham are not in action for three weeks now, due to the FA Cup next weekend and the worldwide break. "It's important now to know that we need to fight a lot until the end of the season. Ours is a lower one and we have to rise it".
"No, no. I think it's not an excuse. But I still love Southampton, of course I want to beat them on Saturday but I wish them the best". "The second half we did not take it seriously".
Pochettino feels the result shows Spurs must accept they are not yet among the top sides in the world, with the club announcing this week that their new stadium will finally be ready to host matches next month. Next time need two offside goal and a penalty.