Morgan’s first goal of the season was enough to secure Leicester’s fourth successive 1-0 win and came after 38 minutes when he out-jumped Jordy Clasie to power Christian Fuchs’s cross past Fraser Forster.
The victory moved them on to 69 points with six matches remaining, seven more than Spurs who drew 1-1 with Liverpool on Saturday.
Leicester manager Claudio Ranieri told Sky Sports: “Clean sheet, three points, step by step. It’s fantastic because we know very well Southampton came here with a lot of confidence.
“I said to the players, it’s the chairman’s birthday, he needs a special present from us. The skipper came back from a long journey with the national team, it’s amazing.
“We are dreaming, if we fight we can do something and we must continue. It’s important to stay very calm and maintain our feet on the ground.”
Morgan said Leicester were determined to take advantage of Spurs’ result at Anfield by beating Southampton in front of their own fans at the King Power Stadium.
“After the game yesterday ended in a draw we wanted to make the most of our opportunity and it’s a massive three points for us today,” he told Sky Sports.
“We had to dig in deep and had a lot of defending to do but we really wanted it today and to get a goal was fantastic.”
Southampton arrived buoyed up by wins over Stoke City and Liverpool in their last two matches and, with the realistic aim of Europa League football next season in their grasp, were seeking to keep their own momentum going.
They should have taken the lead six minutes before Leicester struck when Sadio Mane raced clear of a high defensive line but after rounding keeper Kasper Schmeichel his shot was blocked by Danny Simpson.
The ball hit Simpson’s arm as it was cleared but he denied he had handled the ball intentionally.
“I thought my arm was in my body, I didn’t think it was out and he chipped it up at me and I tried to get in the way of it,” he told Sky.
Saints defender Jose Fonte was saved the embarrassment of putting through his own goal by an athletic leap from Forster in the second half and the Southampton keeper also saved from Simpson, who wasted a great opportunity to score his first goal for Leicester in the closing stages.
Despite Saints’ late bombardment of the Leicester goal, the Foxes’ defence held firm without conceding for the seventh time in their last 10 matches to move them ever closer to the ultimate prize in English soccer.
Original source: Foxes beat Saints to open gap at top