كتب : Hatem Maher
Scott McDonald stunned the Red Devils after 13 minutes when he opened the scoring in a superb fashion.
Gary Caldwell headed the ball back towards the penalty area after United's defense partially cleared a free-kick.
McDonald gathered the ball before deftly lobbing United's keeper Ben Foster, who deputized for the rested Edwin van der Sar.
The visitors piled on pressure afterwards and Celtic sat back to defend their advantage.
Celtic keeper Artur Boruc pulled off a string of superb saves to deny United forwards on numerous occasions.
But veteran winger Giggs came to United's rescue six minutes from time to secure a share of spoils.
The Welsh was the quickest to react to head the rebound after Cristiano Ronaldo's powerful drive was parried by Boruc.
Champions League holders United are in pole position to reach the competition's knockout phase.
They are on top of Group E with eight points from four games, ahead of second-placed Villarreal on goal difference.
Spain's Villarreal are also close to advancing to the next round following their 2-2 away draw with Danish side Aalborg.
Giuseppe Rossi headed the Yellow Submarines in front four minutes before the break but Jeppe Curth equalized nine minutes after the restart.
Substitute Guillermo Franco restored Villarreal's advantage in the 75th minute.
Anders Due ensured Aalborg would get something from the game after leveling the score again nine minutes from time.
Watch Celtic-United match goals