James Maddison fired in from a tight angle after 37 minutes, the Foxes midfielder instructing his team-mates to stand back as he performed a socially distanced celebration, before Harvey Barnes added a second deep into second-half stoppage-time.
Victory takes Leicester within one point of leaders Manchester United, who travel to third-placed Liverpool on Sunday, while Southampton are eighth, three points outside the top four.
The Saints dominated in the opening stages and created the first opening when Che Adams stretched the home defence on the counter-attack, while Leicester’s Barnes’ powerful drive forced Alex McCarthy into action with the game’s first shot after 19 minutes.
The visitors, without talisman Danny Ings after the striker tested positive for Covid-19 last week, went close to a response through Ryan Bertrand and Will Smallbone either side of half-time but neither could find a way past Kasper Schmeichel.
In an entertaining conclusion, Stuart Armstrong rattled the Leicester crossbar with an excellent strike from the edge of the penalty area, while Jan Bednarek produced a superb goalline clearance to deny Barnes and the returning McCarthy saved from Jamie Vardy as both sides pushed for a late goal.
It took Leicester until the 95th minute to seal the three points, Barnes calmly slotting past McCarthy on the break.
Leicester manager Brendan Rodgers challenged his side to “disrupt the Premier League hierarchy” after a 2-1 win over Newcastle in their last league outing maintained their top-four hopes.
Victory in this stern test ensured they continue to do just that.
Enjoying their longest unbeaten run of the season, their streak now at six matches in all competitions since defeat by Everton a month ago, Rodgers’ side delivered an assured performance to remain firmly in contention at the top.
Despite their lofty position as the halfway stage approaches, Leicester have struggled at home this campaign – their four defeats at King Power Stadium in 2020-21 is as many as they suffered in the entirety of last season.
Though largely frustrated in the early exchanges as the visitors retained possession, Leicester’s superior quality in attack eventually ensured that record was improved with Maddison turning sharply to meet Youri Tielemans’ through-ball before drilling home.
The in-form Barnes once again impressed and eventually got the goal his performance deserved to equal his best season tally of 10 after just 24 games.
Unlike last season’s post-Christmas collapse, the Foxes are yet to show signs of falling away. Maddison – involved in six of Leicester’s last 12 league goals – and Barnes are easing the pressure on Vardy to deliver every week and there appears the strength in depth to better maintain this challenge.
The only concern for Rodgers at the end of a pleasing night was the sight of Vardy appearing to limp off as he was replaced by Kelechi Iheanacho in the final minutes.
When Southampton claimed victory in the corresponding fixture last January, the 2-1 win marked a remarkable short-term recovery from a club-record defeat by the Foxes less than three months earlier.
One year on, this match served as another reminder of how quickly the Saints are progressing under Ralph Hasenhuttl.
They were, however, unable to set a club top-flight record of seven consecutive away games without defeat in the absence of frontman Ings. That was despite their relative freshness, having not played for 12 days after their FA Cup tie against Shrewsbury Town was postponed last weekend because of a Covid-19 outbreak at the League One club.
Following their impressive 1-0 victory over Liverpool on 4 January, a triumph which left Hasenhuttl with tears in his eyes, Southampton once again applied themselves with commendable determination but ultimately failed to produce in the final third.
Adams ran out of space at the byeline after breaking clear from the halfway line in the game’s first opening, and neither Bertrand nor Smallbone were able to place past Schmeichel as the equaliser their hard work perhaps deserved evaded them.
At the back, Bednarek produced the heroics to keep his side in the game and full-back Kyle Walker-Peters provided a regular outlet on the right, but Southampton, who named four teenagers on their bench because of an injury crisis, have now scored only once in five league games.
That is an obvious concern for Hasenhuttl as he looks to ensure his side do not fade after their promising start. (Courtesy BBC)