Crawley seemed to be in charge when Mike Jones scored from just inside his own half midway through the first half to add to an earlier own goal. Chris Zebroski pulled one back and three minutes into the second half James Hurst was sent off for a professional foul and Adam Chapman levelled from the resultant penalty. Connor Essam then put through his own goal to secure the League Two side's place in the next round.
Richie Barker made five changes to the side that drew 1-1 at Sheffield United on Friday. There were starts for James Hurst, Connor Essam and Mark Connolly while Sergio Torres came into midfield with Emile Sinclair alongside Jamie Proctor up front.
Newport also made five changes from their last league side and there was a familiar face on their bench in former Reds' midfielder Jimmy Dack, who played for the club back in the early 1990s.
Reds threatened first when Sinclair made space for a shot but it lacked power and direction, failing to trouble Jamie Stephens. Newport then threatened from a corner, but Zebroski failed to direct a free header on target.
The home side broke the deadlock in the 12th minute. Nicky Adams forced a terrific save from Stephens at full stretch but when the ball fell to Hurst he produced a terrific cross that Tony James deflected goalwards and SINCLAIR made sure it crossed the line.
Newport were forced to make an early change when Chapman came on for Ismail Yakubu but the visitors were stretched again when Adams' cross-field pass found Hurst in space and he advanced to the edge of the box but fired a powerful shot over the bar. Connolly then put a decent ball into the box and Essam attacked it but his shot went over the top.
James should have made amends for his error on 21 minutes when Chapman made space on the left and delivered a superb cross but the Newport defender failed to make contact in front of an open goal.
It proved an expensive miss with Reds doubling their lead on 21 minutes thanks to a sensational strike by JONES. Stephens' hurried clearance fell to Jones just inside his own half and the midfielder fired it back over him from fully 50 yards to make it 2-0.
Referee Lewis then had to go off with a calf injury and was replaced by assistant Ryan Atkin and to their credit Newport continued to threaten and a neat dummy by Zebroski allowed Danny Crow to get in a shot which went just wide of the left-hand post.
Two minutes before the break the visitors deservedly pulled pne back when Robbie Willmott made a great run to the byline and slid the ball across the face of goal to give ZEBROSKI a tap-in from a yard out.
Newport were right back in it three minutes into the second half. Hurst's header back to Paul Jones was intercepted by Crow and the defender dragged him back inside the box. Hurst was shown a straight red as the last defender and CHAPMAN gave Jones no chance from the resultant penalty, which he drove powerfully down the middle of the goal.
The home side re-adjusted with Josh Simpson slotting in at right back and they nearly responded straight away when Essam met Adams' clever free kick but headed onto the roof of the net. Then on 53 minutes Proctor ran at a retreating defence and his shot flew a yard wide of Stephens' left-hand post.
By then the game had already become stretched with both sides trading attacking blows and it was Newport who took the lead on 61 minutes. Willmott, who had been a constant menace down the left, put in a low cross which Essam could only slice past t the helpless Jones for an own goal. Willmott then had a chance to get a fourth for his side when he raced away from the defence but Jones blocked his shot for a corner.
Dannie Bulman and Andy Drury came on as Reds went to a 4-2-2-1 formation and then the boss threw on the experienced Gary Alexander as a second striker and on 70 minutes Stephens made a brave save inside the six-yard box after Bulman had sent Mat Sadler into the box on a run. Four minutes later Mark Connolly let fly from 25 yards and Stephens made an excellent parry before rescuing his side again, plunging low to his right to keep out Proctor's drive.
Stephens was a spectator when Alexander hit a powerful volley which took a deflection for a corner which Essam headed wide as Reds threw caution to the wind in search of an equaliser. But Newport held on and Crawley's hopes of a decent run in the competition are over.