The visitors dominated possession but struggled to create many clear scoring opportunities until Scholes pounced on a parry from Besiktas keeper Hakan Arikan in the 77th minute.
Michael Carrick went close for United when he fired in a powerful shot after 12 minutes to force a good save from Hakan but the Turkish side's defence restricted United's scoring opportunities for most of the match.
"We expected it to be tough and it was tough as Besiktas are a very hard team to play against. They are organised and the fans gave great backing to team," United manager Alex Ferguson told Turkish broadcaster Star.
"It required good concentration and patience and I think for most of the game we were quite good at that," he said.
The second half started with more promise for the English champions, who went close in a goalmouth scramble before Hakan retrieved the ball but again United failed to translate their control into goals.
United striker Wayne Rooney made his frustration plain to see when he was substituted in the 64th minute, flinging his boots to the floor in the dug-out.
Winger Antonio Valencia shot wide of Hakan's right post from a narrow angle after 70 minutes and United finally capitalised seven minutes later when winger Nani fired in a crisp shot and former England midfielder Scholes headed in the rebound.
Efforts from Besiktas's Serdar Ozkan in the first half and Mert Nobre in the second gave the passionate home supporters hope.
"When looking at Manchester United's attacks 50 percent were a result of our own mistakes," Besiktas coach Mustafa Denizli told a news conference.
"I'm proud of my players. They fought hard for a result. We expected at least a point from the game."
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