The Serbian defender partnered Rio Ferdinand at centre-back but the Red Devils failed to find the breakthrough in attack despite controlling much of the match in Oslo
Danny Welbeck was twice denied by goalkeeper Gudmund Kongshavn in the first half, while Antonio Valencia drove a shot narrowly wide after the break.
Sir Alex Ferguson (who was not at the game) will have been most pleased, however, to see his captain come through an hour of football unscathed after several months on the sideline with a knee injury sustained in December.
United named a strong side for the clash as Mike Phelan took over first-team duties, with Rio Ferdinand reunited with Vidic at centre-back. Valencia and youngster Michael Keane started in the full-back positions, while Wayne Rooney partnered Welbeck in attack.
Paul Scholes and Michael Carrick quickly took control of the ball in the centre of the park, frequently seeking to send the ball into the wide areas where, on the right, Valencia and Nani were linking up to good effect.
Valerenga, though, went closest in the opening 20 minutes, with Serbian midfielder Bojan Zajic releasing a 25-yard shot that swerved across goal and narrowly wide of Anders Lindegaard's left post.
United looked more penetrative after Ashley Young moved to a central position behind Welbeck around the 20-minute mark, with Rooney retreating to the left of midfield. The former Aston Villa man latched on to Nani's cut-back cross but saw his low shot blocked.
Space continued to open up on the wings but the Red Devils could not take advantage of the crossing opportunities presented to them, with two deliveries aimed at the back post by Young the closest Ferguson's team came to breaking the deadlock.
Rooney found the space outside the box to pick out Welbeck's dash across goal with a cross as half-time approached, but the striker could not keep his flicked header down.
The pair combined once more to engineer a neat one-two on the edge of the box only for Welbeck to lose control of the ball as he advanced towards Kongshavn, who rushed out of his six-yard box to smother.
The goalkeeper was to deny Welbeck on two more occasions before the end of the half with a couple of outstanding individual moments. First, he produced a stunning reaction save to beat away the striker's powerful first-time shot from Nani's reverse pass, repeating the feat to palm away a shot to his right after Welbeck had been sent through on goal.
Ahmed Suleiman almost gave the Norwegian team the lead against the run of play on the half-time whistle, beating Valencia to an unpredictable cross that bounced to the back of the penalty area, but the Nigerian sent his header just wide.
Substitute goalkeeper Lars Hirschfeld was immediately called into action after the break, bravely, and successfully, diving at the feet of Nani after the winger had rushed behind the Valerenga defence.
Rooney, quiet for much of the match in Oslo, peeled off his marker to meet Valencia's cross a short time afterwards but could not get over the ball and headed beyond the crossbar.
Phelan introduced Anderson and Shinji Kagawa in an attempt to liven up proceedings around the hour mark, with Welbeck and Vidic making way.
United should have had a penalty when Martin Pusic fouled Nani just inside the box, but the referee judged the offence to have taken place outside of the area and Anderson's free-kick was easily claimed by Hirschfeld.
The two substitutes, Kagawa in particular, certainly added some extra impetus to United's attacking play but Anderson was left rueing his own caution when Young pulled a driven cross back across goal that the arriving Brazilian could not quite reach.
Valerenga counter-attacked on occasion and after Chuma Anene's shot was deflected wide, Rooney preserved his team's clean-sheet by clearing off the line when the forward took advantage of Lindegaard's collision with Carrick to head towards an empty goal.
It was Valencia who came as close as any United player to finding the match's opening goal, bursting forward from right-back to take on Scholes' pass before shooting just wide of the post in a manner reminiscent of his brilliant goal against Blackburn Rovers during the previous campaign.
Kagawa went on to slide a pass just beyond the reach of any of the red shirts lining up in the penalty area before substitute Javier Hernandez failed to get proper contact on Valencia's cross as Valerenga held on to deny the Red Devils victory ahead of Wednesday's marquee friendly against Barcelona.