Gallery: Images from Swansea clash
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A second-half header from Federico Fernandez gave Swansea the points in South Wales.
Villa bossed the first half but couldn't find a breakthrough.
Joleon Lescott drove wide in the early stages as Rémi Garde's side looked to seize the initiative, while Jordan Ayew fired just over from outside the box after dispossessing Jack Cork.
Ciaran Clark glanced a header off target, while Rudy Gestede was denied by Lukasz Fabianski after meeting Jordan Veretout's right-wing cross.
Ashley Williams was also forced to make a well-timed intervention after Gestede connected with an acrobatic volley.
However, Villa were dealt a sucker punch nine minutes into the second half when Fernandez bundled the ball home after beating the onrushing Brad Guzan to Gylfi Sigurdsson's free-kick.
Sadly the away team's search for an equaliser proved fruitless.
Their best chance after the break fell to Lescott, whose close-range header was smothered by Lukasz Fabianski.
Check our our MATCH IMAGES.