Reds produced a superb display at the Den to book their place in the second round of the Capital One Cup.
The visitors twice led through Hope Akpan and Nicky Adams but Millwall hit back to take the game into extra time. There were no further goals but Reds held their nerve in the penalty shoot-out.
Gary Alexander, Dannie Bulman, Kyle McFadzean and David Hunt all scored while Paul Jones produced two fantastic saves to keep out shots from Darius Henderson and Jack Smith to send the travelling fans into raptures.
Richie Barker named a full-strength for his first competitive game in charge with Gary Alexander leading the side out on his return to the Den.
Both sides looked lively in the early stages and Reds had to defend a couple of dangerous situations before Billy Clarke had a decent effort in the fifth minute when he shot wide after Gary Alexander had laid Mat Sadler's cross back into his path.
The visitors won the first corner which Millwall cleared then Josh Simpson had a shooting chance but fired well wide from distance.
Millwall then won two corners of their own but Claude Davis got an important header away before James Henry's 30-yard free kick was pushed out by Paul Jones to Liam Trotter but he failed to keep the ball under control.
But Alexander went close again on 13 minutes when he met Nicky Adams' free kick with a powerful header but it flew just over Maik Taylor's crossbar.
Reds threatened again in the 16th minute with Alexander doing well to tee up Clarke for a shot which was blocked for a corner but a minute later the visitors were in front when AKPAN met an inswinging corner from Adams with a glancing header into the roof of the net.
The Reds fans were in ecstasy and making a great noise as their side continued to set the pace but they had a scare on 23 minutes when Paul Jones failed to claim a corner but Kyle McFadzean managed to clear Darius Henderson's shot.
The reprieve didn't last long though as Reds failed to deal with a cross from the right by Liam Feeney and WARD glanced his header into the bottom corner.
It was a body blow to Reds after such a bright start but they regrouped and Alexander let fly from outside the box on the half-hour but his shot took a deflection and Taylor was able to make a comfortable save. At the other end a spell of Millwall pressure ended with Feeney firing just wide.
The chances continued to come. After a lovely passing move found Adams in space his cross was met by Alexander who couldn't quite time his header enough to prevent it going a yard over the bar.
The second half took a bit of time to warm up but Reds went close again after 51 minutes when Alexander laid Adams' cross into the path of Clarke but he couldn't bring the ball under control six yards out and the Lions managed to clear. Adams then forced Taylor to make a comfortable save with a shot from distance.
The hosts threatened themselves on 56 minutes when Reds failed to clear a diagonal ball which Henderson cushioned into the path of Chris Taylor but he failed to control the ball and Davis cleared.
A moment later, though, Crawley were back in front. Clarke found ADAMSwho cut inside before finding the top left-hand corner with a stunning strike from 25 yards.
Reds thought they had stretched their lead on 64 minutes when a great move down the left ended with Alexander sending a low side-foot shot past Taylor but the assistant's flag was up for an infringement on the home keeper, but it looked an extremely contentious decision.
There was a scare for Reds with 19 minutes left when Henderson nearly punished poor defending but his shot was hacked off the line by Dannie Bulman and from a corner Henderson headed over.
Henderson went close again with 13 minutes to go when his shot from 12 yards flashed just past the right-hand post but with five minutes to go the hosts drew level when Davis failed to deal with a cross from the right which fell to BATT 15 yards out and his shot flew into the top corner.
That meant extra time and Henderson had the ball in the net on 94 minutes but was penalised for a foul on McFadzean while at the other end Akpan let fly from 30 yards but his shot was always going wide.
Reds made their final change when John Akinde came on for Adams and was immediately booked for a foul on Jack Smith as the first period of extra time ended without further goals.
Not surprisingly given it was the first game of the season there were some tired legs at this stage but in the 111th minute Reds had a wonderful chance when Simpson's pass put Akinde clear but he lifted his shot over the bar with only Taylor to beat. With three minutes left Henderson missed an equally good chance, side-footing wide after cutting inside McFadzean.
But with no further goals it went to penalties and Reds held their nerve and Jones produced to great saves to secure a deserved place in the second round.
Reds: Jones, Connolly (sub: Hunt 74), Sadler, McFadzean, Davis, Simpson, Bulman, Adams (Akinde 100), Akpan, Clarke (Torres 83), Alexander. Unused subs: Kuipers, Wassmer, Cooper, Neilson.
4050 (453 Crawley fans)Attendance: