The Foxes were in fine form following the sacking of Craig Shakespeare and could have come away with a more emphatic win. The East-Midlanders went into the lead courtesy of an unfortunate Federico Fernández own goal. Shinji Okazaki doubled the lead only minutes into the second half from an excellent counter-attack.
The home side attempted to fight back as Alfie Mawson cut the deficit with an excellent finish but could not find an elusive equaliser.
Leicester City caretaker boss Michael Appleton made only one change to the team that toiled to a 1-1 draw with West Bromwich Albion on Monday night. Shinji Okazaki replaced Kelechi Iheanacho as the Japanese international partnered Jamie Vardy in attack.
Elsewhere, Paul Clement also made only one alteration to his previous team as on-loan Bayern Munich midfielder Renato Sanches was named in place of the suspended Leroy Fer.
Fast start from Foxes
The former Premier League champions nearly enjoyed the perfect start in Wales. Okazaki connected well with a cross from Marc Albrighton but Łukasz Fabiański scrambled across to palm away.
It was the former Aston Villa man who then had the next chance to open the scoring but his effort was blocked. Jamie Vardy then struck from distance but his effort was tipped over by Fabiański in the Swansea goal.
The Foxes should really have found the net through Wilfred N'didi but the Swans' stopper was again in fine form as he thwarted the Nigerian midfielder.
The East-Midlanders though did not have to wait much longer to score only their second away goal this month. Riyad Mahrez found space on the left-hand side of midfield and danced his way into the penalty area. His cross was not able to find any of his team-mates but the ball deflected off Swansea defender Federico Fernández and into the back of the net.
Swansea manager Paul Clement attempted to react to the Foxes' goal mid-way through the first period as he replaced Leon Britton with Ki Sung-yueng after the break.
The change only served to assist the Foxes though as they doubled their advantage. Breaking quickly from a Swansea free-kick, Marc Albrighton found Mahrez in space who passed across the box to Shinji Okazaki. It was an easy task from then on as the Japanese forward stroked into the empty net.
Swans aim to fly back
The Welsh outfit though did eventually respond through defender Alfie Mawson. The former Barnsley man latched onto Jordan Ayew's flick from a Luciano Narsingh corner and turned before slamming the ball past Kasper Schmeichel and into the net.
Despite considerable Swansea pressure, the East-Midlanders were still a threat at the Liberty Stadium. Vardy probably should have added to his five Premier League goals but failed to beat Fabiański one-on-one before the stopper also stopped Mahrez's effort.
Jordan Ayew found space late in the game and shot from just outside the penalty area but the ball was easily collected by Schmeichel. Substitute Wayne Routledge also went close but lashed his effort into the side-netting.
The Foxes continued to defend stoutly and picked up a well-deserved three points at the Liberty Stadium. As a result, they rise to 13th in the Premier League table ahead of next weekend's clash with Everton while Swansea fall to 15th.