Barnet extended their unbeaten away record and ended Crawley's undefeated home run in the process with an impressive win at the Broadfield Stadium.
Conference top scorer Giuliano Grazioli netted twice and Dean Sinclair scored the other to keep the Bees firmly at the top of the table.
Barnet dominated from the start and should have been far more comfortably ahead than their one-goal advantage at the break.
Sinclair headed straight at Phil Smith when he had the whole goal to aim at before Grazioli squandered an even better chance moments later.
The former Bristol Rovers striker was left alone at the back post from a low cross by Nick Bailey but somehow managed to fire wide from two yards. Grazioli made amends for his howler on the half-hour mark with a superb strike.
Bailey curled in another perfectly flighted ball from the right and Grazioli sent his side-footed volley into the top corner of the net.
Grazioli took just two minutes of the second half to score his 16th of the season. He latched on to a throughball from Sinclair and looked to have over-run the ball before flicking out a toe to lift it over Smith.
The Reds gave themselves some hope in the 68th minute when Danny Davidson pulled one back. Ben Judge found space on the right and crossed for the giant striker to slide in to convert from close range.
However, Sinclair spectacularly rounded off the win for Barnet in the last minute when he smashed home a 20-yard volley.