Brentford, who are looking to strengthen their hold on second place in the League One table, started the match on the front foot and came close to opening the scoring within the first five minutes. Donaldson fired in a low shot from a tight angle and his effort whizzed just past the far post.
Donaldson registered another shot off target moments later when he sent a looping header over the bar from close range.
Crawley gave their 300 travelling supporters momentary cause for excitement just after the quarter-hour, as Matt Tubbs curled a speculative effort narrowly wide.
Brentford swiftly returned to attacking mode and carved out yet another chance for Donaldson, who blazed over from 15 yards following good work from Alan Judge.
Donaldson's frustrating evening then continued as he took a poor touch that allowed goalkeeper Paul Jones to gather the ball.
Jones was called into action once more before the break, as he blocked a Judge header to keep his side, who have lost their last five league matches, level.