Vennegoor of Hesselink gave the visitors the lead before two strikes by Saha put United in front but Shunsuke Nakamura equalized just before the interval.

Ole Gunnar Solskjaer scored the winner early in the second period to hand the English giants a precious win in Group F opener.

The victory put United in charge of the group with three points, leading Benfica and Copenhagen who both have one point after a goalless draw.

Vennegoor stunned the home crowd in the 21st minute when he brilliantly controlled goalkeeper Artur Boruc's long ball in United's own half, capitalizing on Rio Ferdinand's sluggishness before firing a low shot past Edwin van der Sar.

United's Welsh winger Ryan Giggs was awarded a penalty nine minutes later after he rounded Boruc who clipped him down.

In-form Saha stepped-up and converted the ball into the bottom left corner of the net to level the score.

The Frenchman added the second four minutes before the break with a powerful left-footer after being set-up by Paul Scholes.

Nakamura equalized for Celtic just three minutes later after he curled a superb free-kick that sailed over the wall and went into the right-corner.

Solskjaer sealed the victory two minutes after re-start when he scored in the empty net from the rebound after Saha's initial shot was blocked by Boruc.