Ronaldo scored one and had one disallowed at Pride Park
Manchester United strolled into the quarter-finals of the FA Cup with a comfortable victory over Derby.
Darren Fletcher and Ji-Sung Park had early efforts saved before Nani rifled a right-foot shot in from 20 yards.
Cristiano Ronaldo had a goal belatedly ruled out after a consultation between the match officials before Darron Gibson volleyed home from 18 yards.
Ronaldo nodded in a third before Miles Addison headed in for Derby but Danny Wellbeck's late curler secured the win.
United dominated from the kick-off and Gibson, one of seven changes to the side that beat West Ham last time out, demonstrated their intent in the opening minute with a powerful forward run, but his rising drive cleared the bar.
Fletcher was the first to test out Stephen Bywater with a stinging drive from the edge of the box after a neat interchange of passes with Ronaldo and Ryan Giggs.
Nani then turned Rams skipper Paul Connolly inside out down United's left before delivering a deft chip to the back post, but Park's header was palmed away by Bywater.
Derby had half chances of their own, but Rob Hulse fired a volley on the turn just over and directed a header wide before Kris Commons forced United keeper Ben Foster into a low save from a 30-yard free-kick.
But the goal that United's domination deserved duly arrived just before the half hour mark.
The ball was worked across the edge of the box to Nani, via Fletcher and Giggs, and the Portuguese winger cut back in from the left and hit a powerful drive beyond Bywater with his right foot.
Ronaldo thought he had doubled the lead when Foster's quick throw-out was flicked into his path by Giggs and the Portuguese forward raced clear and tucked the ball home.
But as Ronaldo wheeled away in celebration, the assistant referee learned from referee Alan Wiley that Giggs had touched the ball in the build-up and he belatedly, and correctly, raised his flag for offside.
United's second goal, just before half-time, also had a touch of controversy about it.
Gibson lashed in a low volley from 20 yards after Ronaldo's free-kick had hit the wall, but United's Rafael Da Silva, technically in an offside position, had to hurdle the ball before it flashed past Bywater.
Ronaldo scored a legitimate goal immediately after the restart though, powerfully heading Giggs' corner over Gary Teale and into the net.
And United would have added a fourth but for an outstanding double save by Bywater.
Giggs again put Ronaldo through with another neat flick, but the Rams stopper palmed his low shot away and then kicked Fletcher's fiercely hit drive to safety.
Derby refused to be beaten though and deservedly pulled one back when Robbie Savage's quick free-kick found Commons on the right and his centre was headed home by Addison just before the hour mark.
Teale began to make more of a nuisance of himself down the Derby left in the final 30 minutes as the Rams found a renewed confidence, but all too often the final ball into the box was lacking.
The midfielder did test Foster with a low shot that the United keeper turned round the post and from the corner, Addison found himself in space, but headed agonisingly wide.
United had the last say though when Fletcher and Giggs combined again on the edge of the box before the former flicked a pass out to substitute Danny Wellbeck on the left and the 18-year-old curled a first-time shot beyond Bywater.
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