The Serbian maintained a perfect record in the quarterfinals in New York, now 7-0.
On Saturday, he takes on Stanislas Wawrinka, the Swiss man who shocked defending champion Andy Murray in the day’s earlier encounter.
Djokovic finished the match with a forehand out of Youzhny’s reach, roaring with celebration after his two-hour, 34-minute win.
“The atmosphere is electric; the crowd really gets into it,” said Djokovic, who made his 14th Grand Slam semifinal in a row, dating back to Wimbledon 2010. “Mikhail is a great competitor and a fighter who has a tricky game. Credit to him for coming back and I think it was a really enjoyable match.”