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.
5. Ali Jahanbakhsh 6/10
Worked hard in and out of possession but just lacked the cutting edge in the final third. Replaced by Tau on 71 minutes. Didn't quite do enough and unlikely to start at Man City on Wednesday
6. Yves Bissouma 7/10
A typical all-action display from Bissouma and seemed to enjoy a good old fashioned third round tussle on a dodgy pitch. Took a painful knee to the head in the second half as his teammate Webster leapt high for a header. hit the post with his pen
7. Alexis Mac Allister 6/10
A tough after for the Argentina international. Never really got going on a difficult surface. Took a few hefty challenges and had a decent effort well saved in the first half. Replaced by Trossard on 63
8. Pascal Gross 6/10
A solid if unspectacular display from the German. Did his job well in the centre of the park and very tidy in possession. In contention for a starting role at City. Scored his pen.