Reds were held by second-placed Doncaster to a 1-1 draw at the Broadfield Stadium on Monday when they deserved three League One points.
Josh Simpson fired the hosts into a 24th-minute lead but the skipper went off with a serious ankle injury and James Husband levelled just before the break.
Reds dominated the second half but Doncaster defended diligently to keep Richie Barker's side at bay.
Crawley welcomed Doncaster to the Broadfield in front of the Sky cameras hoping to complete their first ever double of the season.
Boss Richie Barker made one change from the Scunthorpe defeat nine days ago, Dannie Bulman replacing Mike Jones in midfield in a 4-3-3 formation which caused the visitors problems throughout.
Both teams started the game cautiously. Joe Walsh registered the first shot on target with a looping header straight at goalkeeper Woods before Billy Clarke had a sight of goal but his shot from 20 yards went over the crossbar.
The game burst into life on the 25th minute mark. Nicky Adams delivered a low ball into the box that eventually broke to the edge of the area for the onrushing Simpson who fired Crawley ahead with a fine right footed half-volley.
The visitors didn’t dwell on the opener and nearly responded with a goal of their own. James Coppinger linked up well with David Cotterill to create some space in the area and his shot narrowly clipped the far post with Paul Jones a spectator.
Captain and goalscorer Simpson was unfortunately carried off with an injury after a challenge in the centre circle and replaced by Sergio Torres, however the Argentinian was powerless to stop Rovers from equalising.
Cotterill once again was the creator when he delivered a whipped ball into the back post which was met by James Husband who headed past Jones to level the scores with 43 minutes played.
Crawley looked the more likely side to regain the lead in the second half. Clarke had a chance at the edge of the area after good play by Torres but his shot went sailing over the bar before the striker also registered an effort that was straight at the keeper.
Clarke then nearly set up Jamie Proctor for his first Crawley goal but his header went inches wide of the post as Reds pushed for a winner.
The hosts were the better side throughout the second half and once again Clarke looked to penetrate the Donny defence but could only toe poke wide after creating space for himself before firing over five minutes from time.
Crawley survived an onslaught of late corners from the visitors, who were certainly the happier side with the point. Doncaster boss Brian Flynn didn't emerge from the dressing room until 50 minutes after the final whistle.