Karleigh Osborne's first goal in a Brentford shirt was enough to help The Bees to a 1-0 away victory in Andy Scott's first game in full-time control.
The young central defender met a Ryan Dickson corner six yards out and knocked the ball home with a combination of head and shoulder to settle the match.
The visitors never looked like losing, particularly once they took the lead, and although Shrewsbury pushed The Bees back they created little of note.
In the first period the home side were almost shot-less as Brentford took control of possession, creating a number of chances.
Alan Connell volleyed narrowly wide early on and could have opened the scoring when he headed a Ricky Shakes cross wide soon after.
Ross Montague was causing the home defence problems with his strength and power, he set up Connell for a shot which was deflected away and fired weakly wide after a nice turn in the early stages.
Glenn Poole shot wide, Shakes had a shot deflected away and Montague headed straight at Shrewsbury stopper Glynn Garner as Brentford dominated.
Garner denied Poole a fifth goal in four games with a smart stop from a curling free kick and Shakes shot over the bar as The Bees broke quickly late in the half.
Shrewsbury offered next to nothing but Marc Tierney could have put them ahead when he tried to chip Ben Hamer but failed to get enough height on the ball.
And from the moment Osborne put The Bees in front seven minutes after half time there only looked like being one winner.
Brentford kept the ball superbly after taking the lead and often left the hosts chasing shadows, limiting them to half chances.
Matthew Heywood was forced into a clearance deep inside his six-yard box when Ben Davies fired across goal and Andy Cooke pulled a shot wide when he latched onto a Dave Hibbert flick.
Brentford had their opportunities to put the game to bed, substitute Sammy Moore linked well with Connell and Gary Smith to set up a chance for Poole, who fired inches over the bar.
Moore fired wide late on and Tierney blasted off target late on as both sides looked for a late goal but The Bees were happy to settle for Osborne's goal and claim their third successive win.
Brentford: Hamer; Pead, Heywood, Osborne, Dickson; Shakes (sub Moore 78 mins), O'Connor, Smith, Poole; Connell, Montague (sub Mousinho 89 mins)
Subs (not used): Masters, Sinclair, Charles
Shrewsbury Town: Garner; Moss (sub Pugh h/t), Kempson, Langmead; Herd, Davies, Hall (sub Humphrey 67 mins), McIntyre, Tierney; Hibbert (sub Symes 73 mins), Cooke
Subs (not used): Ashton, Esson
Bookings: McIntyre (44 mins)
Attendance: 5,083 (409 Bees fans)
Written by Chris Wickham