Despite a lamentable first-half display, the Red Imps could have gone ahead inside the first five seconds. Brentford captain John Mackie badly under-hit his back-pass, forcing goalkeeper Simon Brown to clear.
He beat Louis Dodds to the ball only for it to rebound inches wide of the right-hand post.
After the early mishap, the first half was nearly all one-way traffic. On 11 minutes, Alan Connell's 20-yard shot deflected off Jamie Hand but just beat the bar.
From the resulting corner, Kevin O'Connor's overhead effort beat the bar and the keeper from eight yards.
Two minutes later, Glenn Poole skillfully worked his way into the box and squared the ball to Lee Thorpe who should have done better from three yards.
On 24 minutes Charlie Ide drove an 18-yard shot towards goal, the ball having rebounded to him after a failed wall-pass with Connell, but the striker's shot was a foot wide of the left-hand post.
On 30 minutes Lee Beevers shot straight at Brown from five yards with the goal at his mercy.
Brentford maintained their ineffective ascendancy in the second half. On 50 minutes Poole's spectacular 25-yard drive fizzed over the bar, and a minute later Thorpe again went AWOL when Ide crossed across the face of the goal.
On 73 minutes Connell headed onto the post from a Lewis Emanuel cross. The Bees finally stung Lincoln on 80 minutes when substitute Moore headed home Emanuel's cross from three yards.
In the final seconds Poole hit the woodwork again for Brentford, and Lincoln's late pressure was too little, too late.