Wilfried Ndidi and Jamie Vardy were on target for Leicester, with Vardy also missing a penalty, as the Foxes edged past their Midlands rivals who are bound for the playoffs.
With three games remaining, Enzo Maresca's Leicester team have 91 points, two ahead of second-placed Ipswich Town, while third-placed Leeds have 87.
Southampton could have moved level on points with Leeds but suffered a 2-1 defeat at Cardiff despite taking the lead.
Joe Aribo's 12th-minute strike put the visitors ahead and they should have increased their lead.
But Saints were made to pay for wasteful finishing after the break as Famara Diedhiou equalised and Cian Ashford won it for Cardiff deep in stoppage time with a deflected shot.
Leicester host Southampton on Tuesday after Leeds visit Middlesbrough on Monday.
