John Gregory made three changes to Tuesday night's starting XI with Jamie Proctor and Dannie Bulman coming in and Joe Walsh returning from international duty with Wales. The trio came in for the absent Josh Simpson, Hiram Boateng and Mark Connolly respectively.
Reds started on the front foot and just minutes into the game Proctor's header just failed to find Matt Tubbs at the back post.
Up the other end, a Jake Hessenthaler corner was flicked on by Craig Fagan. The ball flew across Paul Jones' six-yard box and Crawley were lucky that centre back Leon Legge smashed the ball high into the travelling Reds fans behind the goal.
After 15 minutes, Reds had a great chance to go 1-0 up when Mike Jones' dinked cross found Billy Clarke at the back post. Unfortunately for Clarke, he hit his effort inches wide of Stuart Nelson's right-hand post when the Crawley forward should have scored.
It was to be a poor next ten minutes or so with neither team having too many clear chances to open the scoring at Priestfield.
Just before the half hour mark, an intelligent counter attack saw Proctor lead the breakaway, running from his own half before finding Clarke on the left. However, the Irish striker blazed over the bar.
Just minutes later and Gillingham had a great chance. Another Hessenthaler corner caused mayhem in the box, and after Paul Jones failed to collect, Gills loanee Joe Pigott saw his left-footed effort fly narrowly over the bar from eight yards out.
With ten minutes of the first half remaining Reds had two great chances when firstly, Clarke's effort tested Nelson, and then, after Proctor cut in from the left, his deflected effort spun towards the back post and once more, Tubbs was just inches away from connecting.
From the resulting corner, Mat Sadler volleyed over the bar from a neat corner routine from Andy Drury as Crawley upped the ante.
The visitors had another opportunity when an in-swinging Drury corner found the head of Kyle McFadzean but the defender's accuracy was off and the ball sailed over Nelson's goal - which was leading a charmed life as half-time loomed.
With just minutes of the half remaining, Pigott smashed over again when well placed, and moments later, referee Dean Whitestone blew the whistle and both teams went in at the break 0-0.
Crawley began the second half well and nice intricate play between Clarke and Proctor saw the former slice his cross over Nelson's bar.
Tubbs had two chances just five minutes after the break, and after driving a shot over the bar, had a strike that tested Nelson down low.
The gangly Legge headed over from another corner kick and the ex-Lewes man really should have tested Paul Jones.
Crawley were knocking on the door and Clarke's effort was brilliantly blocked by Adam Barrett before Tubbs' shot was cleared off the line by Hessenthaler as the clock hit minute 60.
Gillingham worked their best chance of the game when Paul Jones pulled off a tremendous save to deny Cody McDonald, getting his fingertips to McDonald's strike before Myles Weston dragged an effort wide.
Jones pulled off another good save to deny a McDonald volley as the game opened up a little.
Proctor leaned back and scooped a chance over the bar after an excellent pull back by Mike Jones. Tubbs then had his on target bicycle kick cleared by Joe Martin.
The travelling Crawley faithful got their first glimpse of Rory Fallon as he came on for Proctor on 72 minutes.
With almost ten minutes of the game remaining, McDonald saw his effort saved well by Jones.
On 82 minutes, Fallon's header almost rolled into the path of Tubbs but the impressive Hessenthaler did really well to nick the ball off the foot of Tubbs and out for a corner.
Two minutes later and Crawley have two great opportunities to win the game but Walsh's header hit the post from a Drury corner and then Clarke should have scored at the far post from another ball in from Drury.
With three minutes remaining the home side did take the lead when a corner wasn't dealt with and substitute Charlie Lee mis-kicked his effort and it somehow finally found a way past the man on the post and into the back of the net.
There wasn't enough time for Crawley to get back in the game and Lee's strike proved the difference. A disappointing result but another opportunity to begin another unbeaten run on Tuesday evening at Shrewsbury Town.
REDS : P. Jones; P. Connolly, McFadzean, Walsh, Sadler; M. Jones (Kaikai, 88), Drury (c), Bulman, Clarke; Proctor (Fallon, 72), Tubbs