The game began with a bang and Brentford saw Damien Spencer stretchered off after an aerial challenge from Darlington defender Alan White in the second minute of the game.
Referee Rob Shoebridge saw the challenge as a straight red card against the Darlington man and the hosts were quickly chasing the game as Brentford looked to secure the points.
The goal that eased the Brentford nerves came from captain Alan Bennett in the 35th minute. A Bees corner from Sam Wood was only half-cleared by the home defence and Bennett fired a low drive past Przemyslaw Kazimierczak from ten yards out.
Worse was to come for the hosts in the 43rd minute when Clarke, a former Darlington loanee, increased the Brentford lead with a close-range header from a David Hunt free kick.
Clarke then secured the win for Brentford when he fired in his second goal of the game and 18th of the season in the 53rd minute. A solo effort saw him dribble his way into the area, before firing a low left-foot drive into the far corner of the net.
Pawel Abbott gave Darlo a glimmer of hope when he latched onto a long ball out of defence and fired under Hamer from six yards in the 59th minute.
Three minutes from time Brentford substitute Sam Williams saw his close-range header cleared off the line by Neil Austin, but the Bees had done enough to celebrate wildly as the final whistle blew.
Click here for a game by game rundown of Clarke's season to date.