The former Dagenham hitman nodded home in the 42nd minute of Saturday’s League One encounter but tempers flared after the break as Gills defender Josh Gowling and Bees striker Charlie MacDonald both saw red.
Gillingham dominated the opening half with on-loan Manchester United strike Febian Brandy seeing a shot deflected wide by Leon Legge and a volley saved by Lewis Price inside the opening 20 minutes.
But the Bees took a shock lead shortly before the break. Myles Weston’s left-wing cross found MacDonald with time and space in the box and his shot hit Mark Bentley but fell kindly for Strevens to beat the despairing dive of Alan Julian.
The hosts suffered another setback five minutes after the interval when Gowling was sent off for a second booking after clattering into MacDonald. But MacDonald followed Gowling down the tunnel in the 65th minute when he stupidly scythed down sub Tom Wynter and picked up his second yellow.
Gillingham dominated the closing stages but they couldn’t force a leveller with Brandy’s lob being hacked off the line by Danny Foster as Brentford held-on.