Miles Addison marked his first start after 12 months of injury hell by canceling out Craig McAllister’s first-half opener with a 62nd-minute header.
But Derby, who missed a penalty through Kris Commons, saw their hopes of a replay snuffed out in stoppage time when Torres converted Dean Howell’s corner to put the Blue Square Premier side through.
Commons spurned the perfect chance to fire Derby ahead in the ninth minute when his tame penalty was saved by Michel Kuipers after the Dutch goalkeeper brought down Chris Porter.
The Rams were punished 20 minutes later when, with a strong wind at his back, Kuipers sent down a huge clearance that caused chaos in the Derby box and the ball fell to McAllister who fired the Red Devils ahead.
Crawley were lucky to reach the break with 11 men on the field when sought-after striker Matt Tubbs escaped with a booking for a two-footed lunge on Robbie Savage.
Derby were back level after 62 minutes when Commons curled in a wicked free-kick for Addison to head home only for Torres to strike at the death.
* RANGERS eased into the fifth round of the Scottish Cup with 3-0 victory over Kilmarnock last night.
The home side went in front when Lee McCulloch picked up Kyle Lafferty’s lay-off to rifle the ball into the net.
Lafferty himself doubled his side’s advantage with an almost identical strike from the edge of the box.
And Steven Whittaker sealed the win, converting a penalty after Jamie Hamill upended Vladimir Weiss in the box.
CRAWLEY TOWN: Kuipers, Wilson, McFadzean, Mills, Howell, Neilson (Hunt 73), Smith (Cook 90), Bulman, Torres, Tubbs, McAllister (Brodie 67).
DERBY: Bywater, Brayford, Green, Barker, Roberts (Davies 90), Bailey, Savage (Moxey 84), Addison, Pringle (Cywka 62), Porter, Commons.
Referee: Mark Haywood (W Yorkshire).