Tamworth recorded their second successive home victory thanks to a stunning strike from midfielder Marcus Ebdon after just four minutes.
The former Everton star picked up a loose ball on the edge of the area from a half cleared free-kick and drilled a low shot into the far corner of the net past Phil Smith.
The Lambs, who have now won three of their last four league games, went on to dominate the first half and should have gone in at the interval with a larger advantage over a Crawley side who have won just once on their travels this season.
Player-manager Mark Cooper and striker Shaun Harrad both missed the target with headers from set-pieces and veteran striker Bob Taylor released Harrad with only the keeper to beat, but his first touch allowed Ryan Palmer to recover.
Just before the break, Scott Stamps was on the end of a flowing Tamworth move but his shot was comfortable for Smith.
As the conditions deteriorated so did Tamworth as an attacking strength and the visitors dominated the second half.
However, they struggled to prize open a solid Lambs defence and only broke through on two occasions.
In the 53rd minute, Allan Tait wriggled to the byline and fired in a low cross that Tamworth defender Adie Smith deflected past keeper Ryan Price, but Dave Robinson was on hand to clear off the line.
Then Tait squandered a golden opportunity on 79 minutes when he followed up a Danny Marney shot that was spilled by Price, but fired across goal and beyond the far post.