Vidic completed an hour in his first outing since recovering from a cruciate operation and was joined by Wayne Rooney, Danny Welbeck, Nani and Ashley Young, all playing their first games since Euro 2012.
Veteran midfielder Paul Scholes had an early shot blocked before Valerenga went close with a 30-yard effort from Mohammed Fellah.
England star Welbeck then wasted a trio of chances as he curled a shot wide, had a volley deflected past the woodwork and nodded a Rooney cross over the bar.
The home side thought they had scored but Chuma Anene's header was dramatically cleared off the line by Rooney.
Shinji Kagawa impressed as a substitute and pulled the strings as United pressed forward with Antonio Valencia, Anderson and Javier Hernandez all going close to grabbing late winners.
United now travel to Sweden for a high-profile clash with Spanish giants Barcelona in Gothenburg on Wednesday .