Chelsea had taken a third minute lead when William Gallas touched home Boudewijn Zenden's superb cross, but David Beckham equalised in the 26th minute through David Beckham.
Zenden put The Blues back in front on the stroke of half time with a venomous strike, only for Giggs to peg Chelsea back once again midway through the second period.
The visitors fell behind early when Zenden's free-kick was touched home by Frenchman Gallas, who last scored against United in the Champions League for Marseille.
Such was the pace on the ball that Gallas only needed the merest of touches, although Roy Carroll did look awkward in failing to prevent it going into the net.
The home side were largely on top in the first half, despite John O'Shea looking assured at the heart of the visitors' defence, and Jimmy Floyd Hasselbaink went close to doubling Chelsea's lead when he flashed a superb shot wide, ten minutes after they had taken the lead.
However, a brilliant crossfield pass from Mikael Silvestre to Beckham allowed the England skipper to go on and score, cutting past Celestine Babayaro and hitting a left foot shot that looped over Carlo Cudicini and into the net after 26 minutes.
Up till then Beckham had been having a poor game, often failing to get his set-piece over the first man and he still failed to convince with his performance after his goal.
A great through ball by Zenden should have seen Chelsea retake the lead with ten minutes to go in the first half, only for Hasselbaink's's touch to desert him and give Carroll the chance to mop up.
Giggs hit the post after good work from Paul Scholes and Beckham on the right, only for the ball to get stuck under the winger's feet and having dug it out, failed to curl it past defender, keeper and into the net.
A poor throw out from Carroll gave Chelsea to launch one last attack in the first period and they made it count, Zenden played the ball in from the right and never stopped running. Just as the move looked as though it would break down, the Dutchman stepped in to take control and struck a brilliant shot into the top corner.
If the first half was mainly Chelsea with flashes of United, the second was a complete contrast in the classic 'game of two halves' mould.
Cudicini saved well from Scholes at his near post and Beckham saw a cross float off the frame of the goal as the visitors began to turn the screw.
Scholes was upended by Cudicini but Graeme Poll refused to give a penalty on the hour and as tempers got a little frayed, Beckham and Marcel Desailly found themselves in the referee's notebook.
Eventually United's pressure told and Silvestre got away from Enrique De Lucas on the left and crossed for Giggs to lift his finish over Cudicini.
Although both sides had chances to win, the thrilling game ended with a point for either side.
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Premiership
Chelsea v Manchester United
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