Midfielder Mario Cantaluppi leveled the match in the 38th minute when he volleyed in from close range after the Juventus back four failed to clear the ball.
Basel's impressive Argentine striker Christian Gimenez sealed victory when he latched onto a corner, volleying the ball into the Juventus net in the 92nd minute.
Down-and-out Deportivo La Coruna wiped the smile from Alex Ferguson's face as the Galicians took advantage of Manchester United's complacency to prevail.
Deportivo were already out of the race for the quarterfinals before the kick-off while United had secured their place as group leaders.
Ferguson's grinning face had been plastered all over the English and Spanish newspapers on Tuesday, after his press conference on Monday when he took another swipe at his bitter enemy Arsenal manager Arsene Wenger.
However, it was a grim-faced Scotsman who left the Riazor pitch after the debacle at Deportivo and United's first defeat in this phase of the competition.
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