Adnan Januzaj did well to turn and shoot inside the area after chesting down a high cross on 16 minutes, but his effort was struck straight at Andriy Pyatov in Shakhtar's goal.
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Wayne Rooney bent a free-kick around the wall, but his effort could only hit the side netting with sections of Old Trafford celebrating minutes later.
Shakhtar should have had the lead when a quick counter saw Fred in acres on the edge of the box. However, the Brazilian made a weak connection with the shot and it was easily blocked by Rio Ferdinand.
Ashley Young had United's best chance but the winger lobbed the ball onto the roof of the net with Rooney screaming for a pass inside the six-yard box.
Young went close again towards the end of the half, but the former Aston Villa man could only flash wide with his left foot after Rooney had released him inside the area.