Carlos Tevez scored the other goal for United, which reached the round of 16. United joins defending champion Chelsea, Arsenal and Liverpool in Monday's fifth-round draw. The four powers have won the last 12 FA Cups and 15 out of the last 16.
Robbie Keane gave Tottenham a 24th-minute lead, but Tevez tied the score in the 38th. Ronaldo then scored on a penalty kick in the 69th and added the third with two minutes to go. The Portugal winger has scored 25 goals in his last 21 games.
Tevez scored United's first goal after Tottenham's Michael Dawson failed to head away a looping pass that Ryan Giggs, with his back to goal, controlled and played to the Argentine.
United's Paul Scholes, who has been sidelined because of knee surgery, returned for his first game since Oct. 20 as a second-half substitute for Michael Carrick just before the hosts went ahead.
Rooney collected a long clearance from goalkeeper Edwin van der Sar and Dawson handled the ball while trying to stop the striker from shooting. Dawson was sent off and Ronaldo converted the penalty kick. Ronaldo made it 3-1 in the 88th with a low shot under goalkeeper Radek Cerny.