Muskwe’s brace in Whetstone bookended a red card for Swans centre back Jack Bainbridge and further cements what has been a hugely encouraging start to the new season for the Club's Under-23s.
The Foxes are now unbeaten in six in all competitions - winning five of those - ahead of Sunday's showdown with early leaders Liverpool at Prunton Park (1pm kick-off).
Steve Beaglehole made just one change to the starting XI who returned from Tottenham Hotspur with a 1-1 draw, with Muskwe replacing winger Layton Ndukwu for the clash.
After a hotly-contested opening, City took the lead inside just 12 minutes.
Muskwe’s hopeful header - straight from Max Bramley’s forward ball - slipped through the grasp of Swans goalkeeper Gregor Zebret from the edge of the box.
It was undoubtedly a fortuitous moment for Beaglehole’s side, but they have earned their share of good luck this term with a string of impressive outings in all competitions.
Chances were few and far between during a first half that often became bogged down in midfield. The hosts, however, were to be handed another slice of fortune just before the interval.
With two minutes to spare, Bainbridge was dismissed for a high boot, which struck Josh Gordon’s face, forcing the visitors to re-evaluate their stratagem at the break.
Swans boss Gary Richards made a double switch in an attempt to alleviate the strain on his side with Jack Evans and Daniel James making way for Jordan Garrick and Brandon Cooper.
The Foxes enjoyed greater freedom in possession during the second period, in front of Caretaker Manager Michael Appleton, who sat among 443 members of the Blue Army in Whetstone.
Liandro Martis entered the fray just before the hour-mark and within two minutes of his introduction, the Curacao international made a key contribution.
After an excellent turn from Thomas, the former Coventry City midfielder found Martis on the flanks who, in turn, fed Muskwe to tap it into the bottom corner and double City’s lead.
Major moment
While Swansea may have felt aggrieved to lose a man at such a pivotal point in the match, Bainbridge’s dismissal undoubtedly proved to be a crucial flashpoint at Holmes Park.
It allowed City, who already had a one-goal lead, to express themselves in the final third – something they did to perfection on 58 minutes for Muskwe’s second.
Who impressed?
"A constant threat." - John Dunn.
"A handful all night." - Steve Guppy.
The LCFC TV commentary duo were in no doubts who impressed most.
Muskwe, now City’s top scorer with five goals to his name, was at his menacing best to keep Swansea guessing with a display typical of his explosive start to the new campaign.
The Development Squad’s hottest attacking force last season, even though he missed the last three months through injury, he refused to give the visitors a moment of peace in advanced positions.
Where do we stand?
On the back of their fourth league victory of the campaign, the Foxes climb to fourth in the PL2 standings, level on points with West Ham United.
City are now seven points adrift of leaders Liverpool and seven ahead of Chelsea, who occupy a relegation berth in 11th place.
Coming up…
For City, a trip to Prenton Park to face unbeaten leaders Liverpool in Premier League 2 awaits them on Sunday afternoon (1pm kick-off).
The following Tuesday, it is Leicester’s final Northern Group A fixture, away at Morecambe, where they will likely need a positive result to confirm safe passage to the knockout phase.
The details…
City: Bramley, Wood, Knight, Hughes, Dewsbury-Hall (Ndukwu 78), Choudhury (c), Johnson, Muskwe, Thomas, Gordon (Kaba Sherif 68), Eppiah (Martis 56).
Subs not used: Iversen, Pascanu.
Goals: Muskwe 14, 58.
Swansea: Zabret, Reid, Lewis, Evans (Cooper 45), Harries, Bainbridge, James (Garrick 45), King (c), Baker-Richardson (Cullen 69), Byres, Gorre.
Subs not used: Thomas, Maric.
Referee: Marc Edwards
Attendance: 443