The Argentine striker was played through by Kaka to score after 21 minutes but despite their dominance Real struggled to add to their lead and they were whistled off by the Bernabeu at the end.
The biggest cheer of the night came when Cristiano Ronaldo replaced Raul midway through the second half, returning to action after two months out with an ankle injury.
"I am concerned with the quality of our play. I don't like this type of football and it's not style of play I want from the team," Real coach Manuel Pellegrini said.
"We just lacked the second goal which would have settled us and allowed us to open up. With only a one goal advantage the game was tightly balanced. The important thing was the win today."
The Brazilian, who had already had a long-range effort saved, danced past two players before slipping the ball into the area for Higuain and the Argentine beat Johnny Leoni with a low shot.
SUPERB VOLLEY
Xabi Alonso stung Leoni's hands with fierce drive and Marcelo cracked a superb volley against the post at a corner, but there was little else to cheer a chilly stadium.
Zurich coach Bernard Challandes said: "Bearing in mind the last few weeks where we have not been doing so well in the league at home we are relatively pleased.
"We were up against the richest team in the world and we weren't humiliated. Our confidence wasn't high and it's an acceptable result for us."
