The game looked to be heading for a stalemate before Dave Woozley broke the deadlock 11 minutes from time with his first goal for Reds.
Steve Burton then gave the home side a flattering win with a double soon after.
To make matters worse for the Lambs, defender Matt Redmile was sent off after the final whistle for something he said to an assistant referee.
It completed a frustrating afternoon for Redmile, who had earlier twice gone close to scoring.
He also put Tamworth ahead after 26 minutes when he headed against the outside of a post from a free-kick. The big defender then had a goal ruled out early in the second half when he was penalised for a push on Ben Judge before nodding home.
Crawley dominated the late stages and a scrappy finale came alive when Woozley struck with a glancing header from Tony Scully's cross.
Burton put the result beyond doubt four minutes from time when he beat the offside trap and slotted through keeper Scott Bevan's legs.
He scored a similar second in injury time, running clear of a static defence and coolly side-footing the ball into the bottom corner.
Steve Burton then gave the home side a flattering win with a double soon after.
To make matters worse for the Lambs, defender Matt Redmile was sent off after the final whistle for something he said to an assistant referee.
It completed a frustrating afternoon for Redmile, who had earlier twice gone close to scoring.
He also put Tamworth ahead after 26 minutes when he headed against the outside of a post from a free-kick. The big defender then had a goal ruled out early in the second half when he was penalised for a push on Ben Judge before nodding home.
Crawley dominated the late stages and a scrappy finale came alive when Woozley struck with a glancing header from Tony Scully's cross.
Burton put the result beyond doubt four minutes from time when he beat the offside trap and slotted through keeper Scott Bevan's legs.
He scored a similar second in injury time, running clear of a static defence and coolly side-footing the ball into the bottom corner.