Ronaldo reacted smartly in the 48th minute after his low shot was saved by goalkeeper Ricardo Lopez and poked the ball to Carvalho for the former Chelsea defender to fire into a gaping net.
"It was our first game of the season at the Bernabeu and I wanted to help my team-mates," Carvalho told reporters. "That's why I pushed forward to try to score."
Some of Real's demanding fans whistled Mourinho and the players after a frustrating first period but there was much more urgency about the team in the second half and they created lots of scoring chances.
Real's opening-day 0-0 draw at Real Mallorca was something of a comedown after the pre-season build up and Mourinho reacted by saying he was a soccer coach and not a magician.
"If people want to whistle then they can and I understand that people want more," the Portuguese said on Saturday.
"Maybe it wasn't a great match and there wasn't a great quality of play, even if we were better in the second half.
"We controlled the match easily and the only thing that was missing was calm and clarity which will come with hard work."
Mourinho brought the 32-year-old Carvalho to the Bernabeu after replacing Manuel Pellegrini as coach at the end of last season.
He also took Carvalho from Porto to Chelsea with him following the Portuguese team's 2004 Champions League triumph.
