Newport manager Mike Flynn is dreaming of an FA Cup trip to Anfield after his Sky Bet League Two side sent Leeds spinning out.
Leeds, 53 places higher on the league ladder than Newport, led 1-0 for most of a pulsating third-round tie at Rodney Parade.
But a Conor Shaugnessy own goal and substitute Shawn McCoulsky's towering header put County in the fourth round for the first time since the 1978-79 season.
A grim afternoon for Leeds got even worse when Samuel Saiz was sent off in stoppage time, the Spaniard banished after allegedly spitting at County midfielder Robbie Willmott.
"I thought we were outstanding throughout, but I knew we were going to put a performance in because they never let me down," said Flynn, who saved Newport from dropping out of the English Football League last season.
Newport trailed to Gaetano Berardi's ninth-minute strike - which possibly brushed off the heel of team-mate Pierre-Michel Lasogga - but created chances throughout.
They finally took advantage of a Leeds side showing nine changes from their New Year's Day draw at Nottingham Forest when Shaugnessy sliced Frank Nouble's cross into his own net 14 minutes from time.
McCoulsky, on loan from Bristol City, then headed home from a last-minute corner to send Rodney Parade wild.