Marcello Trotta's first-half volley against Shrewsbury extended Brentford's winning run to three games and moved them into a play-off spot.
The striker smashed home at the near post after a jinking run and cross from left winger Kadeem Harris.
John Taylor gave Shrewsbury their first attempt on goal just before the break, but his low drive was easily saved by David Button.
Late on Sam Saunders rolled a low cross wide after Clayton Donaldson's pass.
VIEWS FROM THE DRESSING ROOM
Brentford boss Uwe Rosler speaks to BBC London 94.9:
"I thought especially in the first half some of the stuff we played was excellent and we played some fantastic combination football especially for the first goal.
"All credit to Shrewsbury as they didn't just sit back and tried to hit us on the break, they are a good and organised team and you can see why they don't concede many goals.
"Against Stevenage, we shot ourselves in the foot, but now we play a consistent formation and starting 11, confidence is getting better. We still have plenty to do, and we are not at the level of last season but three wins on the trot will help our confidence to get to where we want to be."
Shrewsbury Town Manager Graham Turner told BBC Radio Shropshire:
"The problem for us is scoring goals, and we don't score goals if you stay out of their penalty area. Once again we've defended well and it is the other end that is a cause for concern for us.
"Second half, our performance was better and we should have got something out of the game. We have chop and changed the front two, and we just want them to put it together.
£It is a situation that is a concern and we have to keep working at it.
"The league table doesn't make pleasant reading. We know that if we don't start picking up points it will become depressing."
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