Early Real double defeats Milan
Jose Mourinho's young Real side, playing with energy and pace, dominated an ageing and lacklustre Milan team and cemented their place at the top of the group with a maximum nine points from three matches.
After a fast-paced opening 10 minutes with few clear chances, the in-form Ronaldo struck in the 13th minute with a fierce free-kick that flew through the Milan wall.
With the visitors reeling, he then sprinted in from the left wing to feed Ozil on the edge of the penalty area and the German international's first-time shot ballooned up off the back of central defender Daniele Bonera and into the net.
"The commitment, the work rate, the concentration - the team was fantastic," Mourinho said in a television interview.
"Our goal is to stay top of the group and if we don't lose to Milan in the return match we'll be well on our way to qualifying," added the Portuguese, who left for Madrid after leading Milan's city rivals Inter to a treble of Champions League and Italian league and cup triumphs last season.
Real, who went top of La Liga at the weekend, are flying in their bid for a 10th title in Europe's elite club competition and are yet to concede a goal in this year's edition.
Seven-times European champions Milan, by contrast, are level on four points with Ajax Amsterdam at the halfway stage of the group phase and in danger of missing out on a place in the last 16.
Tuesday's match at a boisterous Bernabeu stadium was briefly interrupted in the first minute when an intruder ran on to the pitch.
The man, wearing a blue Superman t-shirt, evaded security guards for around 20 seconds before being felled by a hefty kick and dragged away.
When play got under way again, Milan were unable to cope with Real's superior strength and speed and quickly fell two goals behind.
Andrea Pirlo, one of six players in Massimiliano Allegri's starting 11 aged 30 or over, was the first of the visitors to threaten the home goal as late as the 29th minute.
Iker Casillas had to be alert to keep out the midfielder's firmly-struck free-kick before former Real player Clarence Seedorf blazed over from a good position wide on the left.
That was as good as it got for Milan and in the second half Real's front four created a string of chances, with Gonzalo Higuain, Ronaldo and Angel Di Maria all going close to a third.
A toothless Milan, with Zlatan Ibrahimovic and Alexandre Pato labouring up front, rarely threatened.
Robinho, another former Real player, who replaced the ineffective Ronaldinho with around 20 minutes remaining, looked lively despite the deafening whistling that rang around the stadium every time he touched the ball.
"There are still six points to play for," Allegri told a news conference.
"We have Ajax and Real Madrid at home and I am convinced we'll go through to the next stage."