Second half substitute Di Maria volleyed home from inside the area nine minutes from time to send Real top of the group standings on six points, two ahead of AC Milan who were held to a 1-1 draw at Ajax Amsterdam.
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The home side were content to reach the interval with a clean sheet after Olivier Sorin pulled off some good saves to deny Marcelo and Cristiano Ronaldo, who cost more than three times Auxerre's 30 million euro annual budget.
"It was a very difficult match, (Auxerre coach) Jean (Fernandez) prepare it very well tactically," Real coach Jose Mourinho told French TV channel Canal Plus.
"It is important to have six points before playing AC Milan, but a draw would maybe have been logical."
"It's kind of Jose to say that. I actually also think a draw would have been well deserved," he said.
Although Real were clearly the better side, they were often stretched by Auxerre's counter-attacking skills. Sergio Ramos and Pepe sometimes proved shaky at the back, especially against long balls.
"Karim has a lot of talent but he needs to play with more character," said Mourinho.
"When I came here, this team had defence problems. Now we are more solid but we still need to find our stride in attack. The players need some time."
Just as an embarrassing goalless draw loomed for Real, Argentine Di Maria chested the ball down in the area before volleying into Sorin's bottom left-hand corner.
