The defeat for Leicester sees them remain five points clear of the dropzone, and Claudio Ranieri will be a concerned man after witnessing his team succumb so easily on the south coast.
Southampton went into this match having failed to win in the top flight since December 18, but from the first whistle they played like a team who should be occupying a place in the top half of the table.
However, it was not long before they fell behind thanks to an exquisite finish from Ward-Prowse, who curled the ball into the far corner of the net from 16 yards after good work from Soares.
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Southampton continued to control proceedings and six minutes before the interval, they netted a second when Ward-Prowse's free kick was headed into the path of Rodriguez, who produced a smart finish at the back post to score his fourth league goal of the season.
Soon after the restart, Pierre-Emile Hojbjerg had the opportunity to put the game out of Leicester's reach but his half-volley from the edge of the area was directed wide of the far post.
The Saints were dealt a blow when Virgil van Dijk was forced off with an ankle injury, but the withdrawal of their skipper did not hinder their performance and Hojbjerg squandered a glorious opportunity on the hour-mark after being gifted the ball by Christian Fuchs but he dragged his shot wide.
Danny Drinkwater volleyed over for Leicester as the game entered the final quarter before the Foxes almost halved the deficit through Wes Morgan, who sent a half-volley into the stands from just eight yards out.
It was a rare moment of success for the Foxes, but Southampton should have had a third goal when Morgan diverted the ball into his own net, but the assistant wrongly adjudged that Maya Yoshida had been in an offside position.
However, Morgan cost his team a goal with five minutes left as he shoved Shane Long to the ground in the penalty area, leaving Tadic to fire the ball into the top corner of the net.
Southampton had further chances to add to their tally but they were made to settle for three as they registered a win which takes them into 11th position in the Premier League table.