Swansea went into the match as leaders, but had defender Alan Tate sent off after only 25 minutes and the Bees took full advantage in front of a bumper crowd of 9,903.
First-half goals from Kevin O'Connor and Eddie Hutchinson did the trick, and although Andy Robinson scored a stunning late consolation effort the result leaves the Bees on a high.
But manager Martin Allen refused to get carried away.
He said: "Of course it feels good to be top, it's the first time for me as manager.
"But I always say don't pop the champagne when you win and don't pop the pills when you lose. There is a long, long way to go."
Allen's side survived a ferocious and hectic first half at Griffin Park, with Swansea losing their discipline with a string of fouls that pushed referee Mr Parkes to the limit.
Lloyd Owusu almost the Bees ahead when his volley from DJ Campbell's cross was saved, but Swansea's demise begun when Tate hacked Sam Tillen to the ground.
That challenge earned him a yellow card and he was off soon after stopping Owusu in his tracks on the edge of the area.
Brentford took full advantage, with O'Connor thumping them ahead from the free-kick. And when Hutchinson made it 2-0 with a header from a Paul Brooker centre they were firmly in charge.
Swans boss Kenny Jackett was fuming with his side's lack of discipline - because Tate's sending-off was the sixth red card shown to a City player already this season.
He said: "We need to do something about it because six red cards is too many for halfway through the season.
"I don't have any complaints about the sending-off, it looked like two bookable offences and none of the players have complained.
"Fair play to Brentford, they started strongly and they were stronger than us through the middle of the pitch. That was the key."
Swansea did better in the second half, dominating possession and eventually making a breakthrough when Robinson's stunning 25-yard shot scorched into the net.
But Brentford's solid defence held firm against ten men.