Adebayo Akinfenwa muscled his way to the opening goal in the 29th minute and when an Andy Robinson cross was deflected in by Bees defender Karleigh Osborne five minutes before the break, the Swans should have gone on to a convincing victory.
Unfortunately, the loss through injury of Darren Pratley and Robinson didn't help and the second period was a poor spectacle.
The Swansea side showed three changes with Robinson, Akinfenwa and Leon Britton all in the starting line-up.
Swansea pressed Brentford back in the early stages, but Robinson fired wide and then Rory Fallon mis-kicked a Marcos Painter cross when well placed.
Akinfenwa, in for the suspended Lee Trundle, showed a good turn of speed to round Kevin O'Connor and cut back inside in the 16th minute but he sent his shot well wide of the visitors' goal.
Two minutes later a Britton shot was palmed out by Nathan Abbey straight to Fallon, but with the goal gaping in front of him he struck the ball over the bar.
Robinson was then back in the action with a superb free-kick that Abbey tipped over at full stretch.
The Swans netted the goal their early display deserved when Dennis Lawrence slipped the ball to Akinfenwa, who brushed aside a couple of weak tackles before chipping over the keeper and into the net.
They went further ahead in fortunate fashion in the 40th minute with Robinson's deflected shot.
It was another poor second-half performance by the Swans and it was not until midway through the half that Swansea looked likely to add to their lead, when Ian Craney's shot on the run was tipped over by Abbey.
The first-half urgency had gone from Swansea's play and the Bees even mounted a few attacks to put pressure on the home defence for the first time in the game.
Overall, it was a poor performance from Swansea and boss Kenny Jackett still has a lot of work to do to keep his side in the promotion reckoning.