Spaniard Llera, signed from Blackpool in January, netted his first goal for the club by curling in from 25 yards in the 53rd minute at the Galpharm Stadium after Danny Batth had been fouled by Sean Morrison.
Nile Ranger, on loan from Newcastle, sealed victory for the Owls in the 72nd minute by out-pacing Tom Clarke to slot the ball past Town goalkeeper Alex Smithies from Jermaine Johnson's through ball.
The result could have been even more emphatic in a game where the home side struggled to get going as Johnson hit the crossbar in only the second minute. Ranger also blazed the rebound wide in front of an empty goal in the 68th minute after Michail Antonio's shot had hit the crossbar.
Town, meanwhile, rarely threatened. Their best effort came in the 63rd minute when Lee Novak forced Owls goalkeeper Stephen Bywater to save his long-distance effort.
The result takes Wednesday six points clear of Huddersfield and moved them into second place, one point ahead of Sheffield United.