After a goalless first half, Egypt captain Ahmed Fathi scored an own goal before Denis Cheryshev struck and Artem Dzyuba added a third.
Ronaldo's shirt is a pretty piece of World Cup memorabilia, however, as the Real Madrid superstar leads the way in the race for the Golden Boot and even became the highest scoring European footballer at worldwide level with 85 goals - one place behind the all-time record.
One the tournament's star performers so far picked up where he left off after his hat-trick against Spain in Portugal's opening 3-3 Group B draw, heading Fernando Santos' men into an early lead with a goal that moved him to 85 worldwide goals - one ahead of the legendary Ferenc Puskas in the all-time standings.
"We knew if we lost we could be out", Ronaldo said.
Renard's team continued to dominate the possession as the match entered its final 15 minutes, but Portugal were remaining strong at the back as they closed on their first win of the tournament.
And he says the Danes are better team than world No.7 France, who pipped Australia 2-1 in the tournament opener.
Ronaldo's success has come at an event in which he has previously struggled to be at his best, and he has eclipsed his goal tally from his combined 13 appearances at his three previous World Cups.
"Of course, no World Cup match is easy even against teams that are theoretically weaker", said Portugal defender Jose Fonte. 'And I hear from Pepe that he asked in the first half if he should have his shirt, what are we talking about?
"We have to run a lot and we have to work hard because this will not be an easy game".