Alex Pritchard put the visitors in front after 11 minutes when he fired a low strike into the corner from 20 yards out.
The visitors were in firm control throughout the first period, and it was Andre Gray who extended their lead when he dinked the ball over goalkeeper Andy Marshall after latching on to Pritchard's through ball.
Cardiff striker Adam le Fondre spurned a great chance to reduce the deficit shortly before the half-hour mark when his close-range effort was diverted wide.
They were made to pay for their profligacy shortly after when Jota made it 3-0 with a powerful effort that deflected in.
The Spanish mdifielder almost made it 4-0 five minutes before the break when his half-volley was saved by Marshall.
Le Fondre was inches away from reaching Noone's delivery on 67 minutes as the Welsh side searched for another goal.
They reduced the deficit further with 15 minutes of normal time remaining, through Kenwyne Jones's close-range finish.
Jones's introduction sparked the fightback and the Trinidad striker went close in the final 10 minutes as the home side fought to restore parity.
However, Brentford held on and took the points at the Cardiff City Stadium to stay in the Championship's top three.