The hard work in the third qualifying round tie was done in last week's first leg by Michael Laudrup's side.
In front of a crowd of 11,538 at the Swedbank Stadion on Thursday evening, goalkeeper Gerhard Tremmel kept a clean sheet to ensure Swansea's passage to the next stage.
Pawel Cibicki gave the Welsh club an early scare when he lashed a shot just wide in the second minute.
Michu and Wayne Routledge also went close to scoring in the first half.
Alejandro Pozuelo freed Michu but the Spaniard's sliding left-footed shot was foiled by the quickly advancing Johan Dahlin.
Routledge failed to convert a better opportunity just a few minutes later. Jose Canas' lovely lofted pass sent the winger racing through on goal but he prodded a right-foot effort wide of the far post.
Wilfried Bony showed them how it should be done with a clinical finish from a Routledge through-ball, but the Ivory Coast international was adjudged to have strayed beyond the last defender.
In truth, Swansea never threatened to reach the level of performance shown in the first leg, but they thought they had the goal their dominance merited late on in a forgettable second half.
Pozuelo's scooped pass played in Jonathan de Guzman and the Dutch international nicked the ball past Dahlin, only for Pontus Jansson to recover and clear off the line.
In the closing stages, Nathan Dyer let fly with a low drive from the edge of the box but saw his effort go just wide of the post.
Swansea will discover their play-off round opponents on Friday when the draw is made in Nyon. Laudrup's side will be among the seeded teams.