Argentine winger Angel di Maria scored in the 53rd minute as Real, playing in an unfamiliar all-red kit, finally beat the inspired Ivan Kelava who produced a string of fine saves in Dinamo's goal.
The only blot on the night for the Spanish team was the 73rd-minute dismissal of left-back Marcelo for diving in the home penalty area. It was his second yellow card.
Coach Jose Mourinho, banned from the touchline, watched Real's opening game of the campaign from high up in the stands.
"It was a good performance in a very difficult away match and we are happy with getting the start we wanted," his assistant Aitor Karanka told a news conference.
Dinamo, playing in the Champions League for the first time since the 1999-2000 campaign, were not overawed by Real and nearly scored in the second minute when Milan Badelj volleyed over from a corner.
Cristiano Ronaldo spurned a good chance a minute later, shooting wide of the far post from 10 metres when he had only the 6ft 5in Kelava to beat.
Karim Benzema then twice went close for Real, his first shot from a tight angle shaving the woodwork before Kelava kept Dinamo on level terms with a brilliant double-save.
The keeper parried a Di Maria effort from close-range and also kept out the rebound, a volley by Mesut Ozil, with a superb reflex stop.
Ante Rukavina almost gave Dinamo the lead against the run of play when he shot straight at keeper Iker Casillas after he was put clean through by a defence-splitting pass down the middle.
Real pinned back the home side after the restart and gained their reward when Di Maria rifled in a left-foot shot from 12 metres after a well-worked move across the edge of the penalty box.
Ronaldo forced another excellent save from Kelava a minute later, the keeper pushing a crisp low shot around the post before also denying Di Maria.
Kelava then rescued Dinamo yet again by saving Benzema's shot with his feet before keeping out a stinging Sergio Ramos effort from 18 metres.
Dinamo piled on the pressure in the closing stages and were almost caught on the break when Ronaldo took a long ball in his stride and forced another stop from Kelava.
Ronaldo limped on to the team bus later having been the target of a series of crunching tackles.
"I really don't understand why Dinamo's players had so much protection from the referee while we had none at all," said the Portugal winger.
"He tolerated hard tackling by Dinamo while he kept reprimanding us for innocuous fouls."
Ronaldo was also sporadically teased by the home fans as they chanted the name of his Barcelona rival Lionel Messi.
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