De Rossi fires Roma into Italian Cup semis
The Italy midfielder drilled home an unstoppable left-foot effort from the edge of the box in the 74th minute shortly after a last-man foul by Blazej Augustyn had left the visitors two players down.
The Sicilians, third-from-bottom in Serie A, already had Giuseppe Bellusci sent off in the 58th for a second yellow card.
Roma soon took command of the quarter-final tie but, with forward Luca Toni injured and captain Francesco Totti rested, the final pass frequently went astray in the first half.
Catania's defence managed to scramble the ball away when their goalkeeper Andrea Campagnolo spilled a crisp John Arne Riise strike and De Rossi shot narrowly wide at the end of a slalom run just before the break.
The Sicilians held out in the second period thanks to some excellent Campagnolo saves until De Rossi struck.
Roma, who have climbed to third in the league after a poor start, will meet the winners of Wednesday's match between AC Milan and Udinese in February's semi-finals.