Mark Quigley's double has put Dundalk in charge after the Setanta Cup semi-final first leg at Solitude.
George McMullan fired Cliftonville ahead on 25 minutes before a superb dipping shot from Quigley brought Dundalk level after 49.
Reds keeper Jack Duffin was at fault as a Daniel Kearns shot got through to make it 2-1.
Another stunning Quigley strike made it a disappointing first game in charge for Reds temporary boss Tommy Breslin.
Eddie Patterson was a spectator in north Belfast just three days after he was sacked as Cliftonville manager.
Dundalk, who had already dumped Linfield and Glentoran out of the competition, were first to go close with Jason Byrne shooting straight at Duffin.
McMullan struck the opener after Rory Donnelly's shot deflected into his path.
Duffin tipped over a Quigley free-kick before the striker levelled from 25 yards.
Ryan Catney almost restored Cliftonville's lead a minute later but his low drive was saved by Peter Cherrie.
Duffin got down too late as Kearns' shot went under his body and into the net after 73 minutes.
Quigley curled in the third with nine minutes left after a one-two with Byrne.
The Irish League side face a massive task to progress when the sides meet again in the second leg on 18 April.