Gorka Pintado scored his first goal of the season as Swansea climbed above play-off rivals Leicester to fourth in the Championship.
The Spaniard struck after 32 minutes when he fired home Nathan Dyer's pull-back from the by-line from six yards.
Pintado and Darren Pratley had further chances but Swansea had to fend off second half pressure from Leicester.
Dorus de Vries saved Paul Gallagher's effort while Lloyd Dyer and Martyn Waghorn both came close.
Swansea have already suffered two defeats at the hands of Leicester this season - on the opening day of the season and in the FA Cup a fortnight ago as Danny N'Guesson scored the winner on both occasions at the Walkers Stadium.
But this is probably the most important victory of all for the Swans who leap-frog Leicester and rivals Cardiff into fourth to keep up the pressure on the top two.
It was Swansea's first win in four league and cup attempts while it was Leicester's first defeat in five.
Leicester had the chance to break the deadlock on 10 minutes when Paul Gallagher's cross found Matty Fryatt but the Foxes' top scorer put his effort just wide.
The Swans enjoyed the better of the possession in the first half and the lively Pintado had a shot blocked before Pratley drove over the bar.
They got the breakthrough on 32 minutes though when Pratley fed Dyer down the right who pulled the ball back from the by-line and Pintado side-footed home from six yards.
Swansea were on the ascendancy and Pratley shot across the face of goal, but Leicester started the second half strongly and really put the hosts under pressure.
Substitute Martyn Waghorn thought he should have had a penalty moments after coming on, on the hour when Joe Allen made contact, but referee Fred Graham waved away appeals.
Swansea were guilty of causing problems for themselves though when first Pratley's mistake was pounced upon and Lloyd Dyer sent a snap-shot past the post.
Then, Garry Monk was caught out and Matt Oakley found Waghorn but he could not control it.
Leicester also threw on Danny N'Guessan and the Frenchman could have punished Swansea had he not missed a glorious chance from six yards out sending a shot wide in front of an open goal.
Swans keeper Dorus de Vries had a relatively quiet game but was called into action late on to punch away Gallagher's effort.
The hosts finished with 10 men when substitute Albert Serran hobbled off in injury time but they held on for an excellent win.
Sousa hails 'massive' Swans win
Swansea manager Paulo Sousa:
"It was a big, massive win for us. I'm proud to work with the players because they deserve this and deserve where we are in this moment.
"A run of goals is something we want and need especially when we control our opponents massively and we create continuous opportunities.
"We believe Gorka can score much more and he knows, like everyone knows, I trust them."
Leicester manager Nigel Pearson:
Leicester manager Nigel Pearson
"I am disappointed but we didn't show enough quality and never passed the ball well enough to retain possession.
"We tried to put pressure on them higher up the field in the second half and it worked to a certain extent with our substitutions making an impact but we couldn't get the goal.
"We have met Swansea three times already this season and after beating them in the two previous matches it is disappointing to come away with nothing to show for it."
Swansea: De Vries, Rangel, Monk, Tate, Bessone (Williams 78), Dyer, Britton, Pratley, Allen (Serran 73), Cotterill, Pintado (Beattie 78). Subs Not Used: Cornell, Trundle, Gower, Butler.
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