Exeter went in front in the seventh minute when Alex Russell’s deep corner was retrieved by Matt Taylor. He laid the ball off to Bertie Cozic, whose 20 yard shot took a deflection past keeper Lewis Price.
Brentford had chances to equalise with Carl Cort firing their best chance narrowly wide, but it was Exeter who increased their lead on the stroke of half-time through Tully.
Craig Noone’s free-kick clipped the wall and the ball found its way to the full-back who hammered a fine first-time volley in off the underside of the crossbar.
Noone made it 3-0 shortly after an hour when he swivelled on the edge of the box and rifled a fine shot into the corner, before City striker Marcus Stewart was sent off for a second bookable offence 19 minutes from time.