Kristian Dennis scored his eighth goal of the season and Jordan Flores added a second just before the end to give Jack Lester a priceless first league win as Chesterfield boss.
From the outset, Chesterfield were the sharper of the two sides, creating chances throughout the 90 minutes. But it took well into the second half for them to break the deadlock and they had to count on several good interventions from keeper Joe Anyon, who recorded his first Spireites clean sheet.
Lester made two changes to the team that stepped up the possession and chance counts against Morecambe, when the improvement in play didn't garner any tangible reward.
Jak McCourt and Chris O'Grady were on the bench with Flores and Sam Hird back in the starting XI. The Spireites lined-up with Scott Wiseman at left-back and with Flores, Andy Kellett and Joe Rowley supporting Dennis in attack for what was only Chesterfield's second visit to the Broadfield Stadium - a 1-1 draw in 2014 being the result of their previous appearance there.
Harry Kewell's side went into the match with just two home wins in their last 17 games but with better away form. They've picked up eight points in their last four excursions, which saw them in a comfortable 18th spot in the table at the start of the match.
Wearing all-blue, Chesterfield fashioned the first meaningful attack of the night with a sweeping counter-attack which saw Dennis, Louis Reed and Wiseman open up the rearguard but Kellett's shot was blocked and flew out for the game's first corner, which was cleared.
Kellett, further up the park than of late, crossed in but keeper Glenn Morris gathered just as Dennis was arriving in the right spot, right in front of the hardy bunch of travelling Spireites.
Dannie Bulman hit high after he'd nicked the ball in a 50-50 but Chesterfield's back line was looking solid in the opening 15 minutes and it was Wiseman who played through for Dennis, but Morris was rapid off his line to clear the danger. Rowley and Flores fashioned an attack, although neither could quite find space for a shot, but the early signs were reasonably positive.
Jordan Roberts' shot was deflected for a corner on the right and Dennis cleared the poorly delivered kick. Crawley won a free-kick as the ball was cleared but Roberts' delivery was poor and Anyon gathered with ease.
Kellett received the ball on the box-edge, on his right foot, but his shot was on target and forced the keeper to stoop low to smother it with 20 on the clock.
Skipper Robbie Weir picked up his fifth yellow of the season - so a suspension is now on the cards - and Anyon had to be sharp to hold Joe McNerney's header from the resulting free-kick as Crawley began to put together their best spell of pressure.
Roberts broke the back-line but couldn't control the ball and Anyon swept up and set up an attack which saw Flores shoot and Morris save. Anyon had to drop quickly to his left to save a shot from home skipper Jimmy Smith and Crawley then won a corner but the whistle went when the ball was in flight and any danger was averted.
Weir set up Dennis for an angled left-footer that was hit well and Morris had to be at his best to fling himself right and gather in the ball in fine style and the keeper matched that stop moments later to deny the same player from closer range.
The Spireites started the second half hoping to add to the largely positive opening 45 which had seen them carve out half a dozen good openings and force Morris to work hard.
Crawley brought on Josh Payne at the break for Mark Connolly; normally a midfielder, the sub slotted in at centre-back.
The hosts won a corner which drifted across the area with little threat as the period began in a more cagey fashion than the first had ended. Flores fed Rowley whose powerful run saw him take a knock as he laid off to Reed to clip a ball for Weir who got in a header but it lacked the power to trouble the keeper. Rowley recovered and resumed.
Flores won a corner on the left, Reed delivered low and Wiseman got in first but was unable to conjure up a shot. Rowley made a wonderful run into the box but he scuffed his shot with a Goal of the Season contender begging. Chesterfield regained possession immediately and Bradley Barry's teasing cross just eluded the gathering blue shirts just shy of the hour-mark.
Chesterfield gifted possession to enable the Red Devils to break and Enzio Boldewijn's cross clipped Wiseman and earned a corner that was solidly dealt with.
Anyon clawed away a Roberts free-kick, an excellent save which was matched at the other end when a fine moved saw Flores shoot towards the corner but Morris flung himself right to paw the ball away.
But on 73 minutes, Morris was powerless to deal with Dennis's shot, who scored a poacher's goal as he pounced on Evatt's nod down from Flores' free-kick.
Crawley soon earned a couple of corners as they sought to get back into the game and Anyon had to save well from Roberts to maintain the lead. Diego De Girolamo came on and his first involvement was to pass into the path of the marauding Flores (88) to fire home his first goal for the club and confirm a first away win since Swindon in March, a win greeted with great glee by the 157 travelling fans.
Crawley: Morris, McNerney, Connolly (Payne 46), Boldewijn, Smith, Roberts, Clifford (Meite 83), Evian, Bulman, Lelan, Lewis (Camara 71), Subs (not used): Mersin, Doherty, Djalo, Tajbakhsh.
Chesterfield: Anyon, Barry, Evatt, Hird, Wiseman, Weir, Reed, Rowley (De Girolamo 88), Kellett (Briggs 77), Flores, Dennis (Dimaio. 85). Subs (not used): Jones, O'Grady, Maguire, McCourt.
Goals: Dennis 73, Flores 88
Referee: Nick Kinseley (Essex)
Bookings: Weir, Rowley (Chesterfield) Camara (Crawley)
Attendance: 1,516 (157 from Chesterfield)