A goal two minutes from time by Toumani Diagouraga earned Brentford a 2-2 draw at Brunton Park just when Carlisle looked to have held on for the three points.
Clarkson had put Bees into an early lead only for James Berrett to level before half-time. Clarkson's own goal looked to have won it for the Cumbrians but in the end it was the home side who were left clinging on.
Carlisle started brightly but were shaken out of their stride when Brentford grabbed a ninth-minute goal through on-loan Bristol City striker Clarkson.
The goal was instigated by a great run down the right from defender Adam Thompson who planted a cross onto the head of Jonathan Douglas whose cushioned header was swept home by Clarkson from eight yards.
Goalkeeper Richard Lee kept Brentford in the lead with a fine one-handed save to deny Liam Noble. But Carlisle drew level in the 23rd minute when Noble drifted beyond the far post to nod Matty Robson's cross back into the danger area where Berrett swooped to side-foot home from six yards.
There was a distinct slice of luck about Carlisle's second in the 62nd minute which came from a free-kick on the right after James Tavernier had been obstructed. Berrett's ball into the box flew off Clarkson and into the net catching Lee unawares.
Brentford thought they had equalised with a header from Diagouraga which was cleared off the line by Francois Zoko. But there was no denying the visitors who took home a share of the spoils despite leaving it late.
Clarkson slipped the ball through to lanky midfielder Diagouraga who beat Carlisle goalkeeper Adam Collin from close-range.
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