Championship minnows Reading looked on course to record another FA Cup shock after two first-half goals from Shane Long put them in firm control.
But a goal from Ashley Young and a quickfire brace from Carew – all in the opening ten minutes of the second period – turned the tables, before Carew completed his treble with a stoppage time penalty.
The Norwegian front man said: “We struggled in the first half and the gaffer gave us some serious words at half-time.
“Ashley Young’s goal was really important for us and from then on I had a great feeling that we were going to win.”
Victory ended O’Neill’s bizarre statistic of never having won a game in the month of March with Villa since he took over from David O’Leary in 2006.