The Ivorian then doubled their advantage in the second half after more good work from Sigurdsson, as Garry Monk's side coasted to their first win since August.
Below, Sports Mole takes a closer look at what happened in Wales tonight, and how it happened.
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On target: 3
On target: 4
Was the result fair?
In a word, yes. Swansea's 1-0 half-time lead was far more comfortable than it seemed due to Leicester's shortcomings in the final third. They never looked like scoring in a first half that saw the Foxes fail to register a single shot on goal and, despite a slight improvement after the break, they never did enough to warrant a result here. Fully deserved three points for the hosts.
Swansea City's performance
Having failed to pick up a Premier League win since August, the result was always far more important than the performance for Swansea. Tonight they got both. Manager Garry Monk will take an enormous amount of satisfaction after watching his side produce a solid display at both ends to earn a much-needed and well-deserved three points.
They were clinical enough to convert one of just two chances in the first half but remained purposeful going forward, while they stood up very well defensively in a second half which saw Leicester come to life a little more. Overall there was plenty of positives for Swansea, who will want to build on this win and hope that it is a catalyst toward recapturing their remarkable early-season form.
Leicester City's performance
It has been 34 days since Nigel Pearson's side beat Manchester 5-3, yet that result looks far more remarkable now than it did then by virtue of their deficiencies in the goalscoring department these days.
They have scored no goals in the three defeats that they have suffered since shocking United, and the Foxes never looked like finding the net here, either. It was more of the same for Leicester tonight, with Leonardo Ulloa again hinting that his early-season heroics might have been a fluke rather than the early stages of a productive career in the top flight, while David Nugent offered little to nothing by way of support.
The marked lack of creative spark signals worrying times for Leicester. It may only be a month or so since that famous win over the Red Devils, but it feels far longer based on their subsequent performances.
Sports Mole's man of the match
Wilfried Bony: The Ivorian came into this one with two Premier League goals from eight outings and a big question mark over his ability to scale the same heights as he did last season. However, Bony answered those questions with aplomb tonight, scoring both goals in a performance that he will hope proves a watershed moment in his season. He will rightly earn plenty of plaudits for the goals tonight, but it was an excellent overall display that has earned him man of the match.
With five Serie A crowns and a Champions League title to his name, Esteban Cambiasso was far and away the most decorated player on the field tonight. Despite all of his accolades, however, the veteran Argentine midfielder still managed to miss two of the most gilt-edged chances he will have all season - and both in quick succession.
First, Cambiasso hit the post from point-blank range after Lukasz Fabianski tipped away an Andy King header, before the Inter Milan legend then failed to convert that rebound in an incident which seemed to sum up Leicester's problems in front of goal recently.
Very quiet evening for Mike Jones, who was afforded the luxury of keeping his cards in his pocket throughout. It could have been different, however, as Dean Hammond elbowed Gylfi Sigurdsson in an aerial challenge which surely would have earned the Leicester midfielder at least a booking had Jones witnessed it.
Swansea City: The Swans face a tricky away trip to Liverpool in the Capital One Cup on Tuesday, before resuming league duties with another visit to Merseyside to face Everton on Saturday.
Leicester City: The Foxes, meanwhile, host West Bromwich Albion at the King Power Stadium next Saturday.