Joe McNerney celebrated his return to the side with the equaliser as Reds maintained their unbeaten start to the EFL 2 campaign.
The defender struck with a simple close-range header midway through the second half after former Crawley striker John Akinde had given Barnet an early lead.
Reds deserved a point for their spirited second-half display but the Bees will feel they should have won it. Akinde himself could have had hat-trick and at times it looked as if last week’s punishing schedule of three away games in a week had caught up with the home side.
Reds made one change to the side which beat Exeter on Tuesday, with McNerney replacing Mark Connolly, who dropped to the bench, but the back four were exposed after just three minutes when Barnet went in front.
A poor clearance by Yusuf Mersin which didn’t reach halfway was headed forward by Sam Togwell and Akinde got goal side of Alex Davey before volleying a right-foot shot into the corner.
Akinde could easily have been celebrating again on two occasions after just 12 minutes. Mersin pushed away his powerful angled drive and then Akinde got in front of McNerney to meet a corner but guided his header just wide of the right-hand post. The set piece came after Mersin had touched a header from Michael Nelson over the bar.
Reds finally began to enjoy some possession of the ball but Barnet continued to carry the greater threat and Jean-Louis Akpa-Akpro headed another corner goalwards but Jimmy Smith headed it off the line.
The hosts managed their first shot on target in the 29th minute when Josh Vickers pushed aside Josh Payne’s side-footer from the edge of the box as Crawley enjoyed their best spell so far.
But Akinde went close again in the 34th minute when he got behind the home defence but his shot from the narrowest of angles rolled across the face of an empty goal. At the other end, Smith’s corner was headed just over by McNerney then James Collins’ pass gave Jason Banton an opportunity for a shot but his effort went well over.
At least now Reds were offering an attacking threat, particularly in the wide areas, but they were nearly punished on the counter four minutes before the break. Alex Nicholls made a great break down the left and found Akinde whose shot on the stretch was blocked by Mersin.
Reds made a double change 11 minutes after the break with Josh Yorwerth and Adi Yussuf replacing Josh Payne and Billy Clifford.
The second half took a long time to get going but McNerney worked Vickers in the 64th minute with a header from Jimmy Smith’s free kick which the Bees’ keeper pushed away for a corner. Two minutes later Vickers was at full stretch again, this time to push Smith’s free kick from the corner of the penalty area over for a corner.
Reds’ pressure paid off midway through the half. Collins’ angled shot crashed back off the underside of the bar after he’d been picked out by Andre Blackman’s angled ball and McNERNEY was on hand to send a simple header into an empty net.
Akpra-Akpo nearly produced a quick response for Barnet, wriggling clear to fire wide of the left-hand post. The visitors were becoming more of a threat and on 75 minutes Bira Dembele’s header from a free kick was deflected wide then substitute Mauro Vilhete stooped to head the corner just wide.
Fourteen minutes from time Matt Harrold came on for Boldewijn but Reds had another let-off when a long throw found Dembele eight yards out and his downward header hit Mersin before Akinde was judged offside as he tried to bundle in the loose ball.
But Reds went close again with seven minutes to go when Banton’s dipping effort from 25 yards only just cleared the crossbar with Vickers struggling.