The hosts have failed to really find their rhythm in the first 45 minutes and chances have been few and far between.
It was a bright start from the visitors as Alexei Kozlov fired just over from 25 yards, before Swansea started to find their feet.
Wilfried Bony and Michu combined well after 21 minutes to release Jonjo Shelvey, but the midfielder sliced his volley horribly wide from just inside the box.
Chico Flores was then called into action, clearing the ball from underneath his own crossbar following a good break from former Liverpool striker Djibril Cisse.
With 10 minutes to go until the break Lorenzo Melgarejo raced clean through on goal and was tugged back by Dwight Tiendalli, but the referee produced a yellow card, much to the anger of the visitors' bench.