Interim manager Michael Appleton believes securing the first goal was crucial for Leicester to leave the Liberty Stadium with all three points.
An own goal from Federico Fernandez and strike from Shinji Okazaki was enough for the win, despite a consolation goal from Alfie Mawson.
It was Leicester's start to the game that impressed Michael Appleton, who took charge following the dismissal of Craig Shakespeare on Tuesday.
Speaking post-match to Sky Sports, Appleton claimed: "Getting the first goal was massive - that is the second time we have done it this year and obviously that is the two wins we have got.
"It was important that we started the game really well as we have not particularly started a few of the games that well of late, and gone behind in games. Delighted at the way they stuck at it as they could quite easily, after they pulled a goal back, gone on to draw or even lose the game."
Leicester were well worth their victory and leapfrog Swansea in the table to 14th, with Paul Clement's side a point and place behind them.
Appleton was also quick to praise the application of the players in what has been a tough week for the club.
He continued, saying: "It's been a difficult week, so obviously we are delighted with that performance, the first half especially.
"I thought the way we moved the ball at times in that first half and it showed in number of gilt-edge chances we created. So to produce a performance like we did today after the week we have had, the players deserve a lot of credit."