The Bhoys had not managed a shot of note when a 13th-minute free-kick on the left-hand side was whipped into a crowded United box, only to be headed clear by the towering Nemanja Vidic.
Yet Celtic refused to give up the move and found a way to force the ball back into the box where Scott McDonald had stayed alert, taking a touch before lifting a beautifully weighted shot over Ben Foster and into the far corner of the net.
If United were galvanised by the goal then the home side were practically electrocuted, finding a new level of energy that prevented last season's Champions League winners from moving the ball around as soon as they entered the opposition half.
United, clearly frustrated by a lack of success through the middle, began to rely on set-pieces for their chances.
Firstly Rio Ferdinand couldn't handle an awkward bounce from a 19th-minute Giggs corner and managed to hack the ball well over the bar from just four yards out.
A series of half-chances came and went before another corner, just before half-time, found Vidic in space but his rushed header from a bouncing ball somehow went over the Celtic bar.
United were clearly the more frustrated by half-time and brought on Dimitar Berbatov for Nani at the break.
The Bulgarian certainly added presence to the United attack, creating another option for the Red Devils through the middle.
Yet it was hard to assess his impact, such was the scale of United's attacking play. Every player had some sort of chance in the second half, just as every Celtic defender put his body on the line to prevent a goal on many occasions.
The effort put in by the Bhoys' back-line, which grew to around seven in the second half, made United's inevitable goal all the more heartbreaking when it finally arrived.
The home side appeared to have subdued Ronaldo's long-range shooting but a swerving 84th-minute effort caught Artur Boruc off guard and his parry fell fatefully to Giggs, who nodded in from close range.
Just as both teams were considering how content they should be with a draw, Berbatov was given the chance to win the game.
Ronaldo headed a ball into the six-yard box where Darren O'Dea missed his clearance, allowing the Bulgarian a free shot which somehow went wide, leaving United with a single point from their trip to Glasgow.