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.
13. Davy Propper 6/10
Came on for Zeqiri and took up his usual central midfield position. Had a golden chance to score soon after he came on but dragged his left-footed effort wide from 15 yards. Scored his pen with ease
14. Percy Tau 6/10
Made his long-awaited debut. Looked lively when he came on and linked well with Neal Maupay. One effort well saved at the near post by King and then blazed a decent chance over the bar in the second period of extra time with his right foot
15. Bernardo 6/10
Replaced Solly March and played well in extra time. One excellent cross from the left that saw Lewis Dunk's header brilliantly saved by Tom King in the Newport goal
16. Joel Veltman
Replaced Ben White with 10 to go.