five minutes before the break.
Nicolai Jorgensen beat keeper Iker Casillas to the ball and his header bounced down off the crossbar before appearing to strike Modric's hand on the line.
The Croatia midfielder was able to clear the danger but there were whistles of discontent from the home fans as the players trooped off at halftime.
Ronaldo, however, settled the nerves in the stands with his second 20 minutes into the second half, his 55th goal on his 94th appearance in Europe's elite club competition and his 26th in his last 21 Champions League outings.
The 2008 World Player of the Year burst into the penalty area and powered Di Maria's clever chipped cross past Wiland.
Di Maria netted a fine curling effort six minutes later after cutting in from the right and another in the first minute of stoppage time as Real secured a maximum six points from their first two matches.
Copenhagen have one point along with Galatasaray who drew 2-2 at Juventus (two points) on Wednesday.
"I am very pleased, we played a great match," said Di Maria. "We changed the system a bit with three players up front.
"We have to keep this up now, we know that all the matches will be tough."
Copenhagen coach Stale Solbakken, whose side have made their worst ever domestic league start this season, said he was pleased with his team's performance until the second goal.
He also suggested the referee should have awarded a spot kick and sent Modric off for the incident on the line late in the first half.
"It could have been a penalty and a red card," said Solbakken. "I can understand the referee didn't give it because it happened very fast.
"I don't blame the referee at all but it could have been a big turning point in the game."
He was full of praise for Ronaldo who was top scorer in the competition with 12 goals last season when Real were knocked out in the semi-finals by eventual runners-up Borussia Dortmund.
"His first one should have been avoided, the second I have seen him do it too many times to blame any of our players,"