Mahrez scored after just seven minutes with a low shot from the edge of the box and added a second 12 minutes later after an error by Saints goalkeeper Paulo Gazzaniga.
The three points were especially important after Sunderland’s win at Everton earlier in the day had left Nigel Pearson’s team outside of the relegation zone on goal difference alone.
Mahrez, who came close to completing a hat-trick in the second half, will get the plaudits but this was a victory built on hard work and intensity by the entire Leicester side and in particular their forwards Jamie Vardy and Leonardo Ulloa.
Both players covered mile after mile in attacking and defensive situations, pressing the Southampton defence in the early stages of the game and then dropping back to assist their own backline as the match went on.
Tactically, Pearson was spot on. His team allowed Southampton to have the ball in their own half and in wide areas, knowing any long passes into the box would be easily consumed by his giant back three of Wes Morgan, Robert Huth and Marcin Wasilewski.
Huth in particular made several vital headers as the visitors, who remain seventh in the Premier League table, were kept at arm’s length. They can have no complaints about the result.
Only in the final stages did they produce any attacking football of real quality but by then the game was won.
Their best chance came in the 71st minute when Sadio Mane struck a looping shot which briefly had Kasper Schmeichel worried but which he pushed over his bar with a degree of comfort.
Results elswhere mean that Burnley have been relegated from the Premier League, taking one of the places which seemed destined to go to Leicester for so long considering they were bottom for four months.
They have almost doubled their points total in the past month and, given that form, now have a strong chance of staying in the division.
Soccer Saturday analysis – Charlie Nicholas
“We know Leicester like to play into the wider areas, a bit of pace. Nigel Pearson has manoeuvred Vardy back into a position that suits his strikers. They threatened in behind the defenders more. He’s pulled another one out the bag today because Mahrez has been on the bench for a few matches now, but he comes on today and scores the two goals.
“The back three were so solid; Schmeichel for me gets better and better. He’s a very cool customer but he introduced Robert Huth as much as Cambiasso. Those two individuals are stunning for them.”
Leicester: Schmeichel (6) Wasilewski (7) Huth (8) Morgan (7) Albrighton (7) James (6) Cambiasso (8) Schlupp (7) Mahrez (8) Vardy (8) Ulloa (8)
Subs used: Nugent (6), Hammond (6)
Southampton: Gazzaniga (5) Clyne (6) Fonte (5) Alderweireld (5) Bertrand (6) Reed (6) Wanyama (5) Steven Davis (5) Mane (6) Elia (5) Pelle (5)
Subs used: Djuricic (5), Long (6)
Man of the match: Robert Huth