Reds suffered their first home league defeat of 2013 but there was a lot to commend their performance on an incident-packed night at the Broadfield.
Crawley could not have made a worse start, losing Mark Connolly in the first minute when he was shown a straight red card for tugging Clayton Donaldson in the box.
Donaldson missed the penalty but by half-time had found the scoresheet when he capitalised on a mix-up between Paul Jones and Connor Essam, who had come on to make his debut in place of Connolly.
That came on 31 minutes and put the Bees 2-0 up. They had taken the lead on 16 when they broke following a Crawley free kick and Bradley Wright-Phillips' pass teed up Sam Saunders who lashed a powerful shot past Paul Jones, the ball taking a slight deflection off Dannie Bulman on the way.
Shell-shocked Reds had competed on equal terms for much of the half without creating too much and at the break top scorer Billy Clarke had to go off with a hamstring tweak.
But Reds went for it in the second half. Aiden O'Brien came on for his debut although in his eagerness to get on had not informed the fourth official and he was promptly shown a yellow card.
On 53 minutes O'Brien nearly got a decisive touch to a cross from Jamie Proctor as Reds got up a head of steam and it became a ten-a-side game on the hour when Adam Forshaw, who had already been booked, dived in the box and was shown a second yellow.
The goal Reds had been threatening arrived on 63 minutes. Nicky Adams took a pass from Mat Sadler and ran at the defence before hitting a curling shot into the top corner from 25 yards. It was a goal worthy of a much higher stage and was his 10th of the season.
Now the boot was firmly on the other foot as Crawley pressed for an equaliser. Any number of free kicks and corners were cleared and Proctor was desperately close to getting his first goal for the club but Moore clawed his deflected shot out of the air.
The referee played seven minutes at the end to add to his three first-half stoppage minutes and then ten men deserved something from 100 minutes of titanic effort but it was not to be. The crowd gave them a standing ovation at the end for their performance and, despite the defeat, it was richly deserved.