Brighton thought they had netted a 90th minute winner when Solly March cracked home a fine low effort from 20 yards that whistled beyond home stopper Tom King.
Newport are never a team to give up in the FA Cup and they equalised on 96 minutes when goalkeeper Jason Steele totally miss-judged a cross from the right and the ball hit Adam Webster and went into his own net.
Steele however redeemed himself in style with four cracking saves in the penalty shoot-out and then Webster tucked home the winning spot kick.
Scroll down and click through to see how they rated out of 10.
1. Jason Steele 8/10
What was he doing for that cross? Lost the ball completely for the Newport leveller. But then saved FOUR penalties in the penalty shoot-out. Incredible from Steele
2. Ben White 7/10
Played well against his old club and looked to push forward and provided nice crosses from the right. One lovely moment in the second half when he nut-megged a defender on the edge of the box. We won't mention the shot that followed. Replaced by Veltman with 10 to go due to a tight looking hamstring
3. Lewis Dunk 8/10
Caught out early with one short back pass but was excellent thereafter. Looked to push forward as Albion dominated possession. Good distribution and a powerful header from a corner well saved. Super clearance off the line after Steele's mishap from a long through ball. Excellent second half header superbly saved by King. Scored his pen.
4. Adam Webster 7/10
Commanding in the air as he dealt well with long throws into the box. Improved no-end in possession of late and always looked to drive Albion forward. Unfortunate own goal but made up for it with the winning penalty