Craig Beattie's injury-time goal denied Motherwell victory in a hugely exciting start to the SPL season.
John Hartson scored a first-half hat-trick comprising two headers and a penalty kick.
Brian Kerr had briefly cancelled out Hartson's first with a fierce drive, but the second half was Motherwell's.
They went 4-3 up through headers from Jim Hamilton, Scott McDonald and then Willie Kinniburgh but sub Beattie prodded in the equaliser.
The game started in torrid fashion, with a series of thunderous challenges and Celtic's young centre half Stephen McManus lucky not to be booked for two of those.
Scott McDonald, the man who cost Celtic the league last season, threatened them again after 12 minutes when he broke free of Stan Varga, but he dragged his shot wide.
But it was Celtic who took the lead shortly afterwards.
Alan Thompson did well to get his cross in under pressure and Hartson easily outjumped Steven Hammell at the back post to head into the net.
But Motherwell scored a sensational equaliser when Alan McCormack, Paul Quinn and Kerr combined superbly to send the latter into the box and he drove a terrific left-foot shot past the despairing dive of David Marshall.
But Hartson restored Celtic's lead with just over half-an-hour gone, craning his neck to turn Aiden McGeady's cross into the corner of the net, though the 41-year-old Gordon Marshall looked slow going down in an attempt to keep the ball out.
Marshall was also at fault as Celtic extended their lead before half time.
The keeper hauled Stilian Petrov down in the box and Hartson gleefully completed his hat-trick from the spot.
John Hartson scored a first-half hat-trick
The excitement continued after the break as Motherwell fought their way back into the match with two goals in three minutes.
First Hamilton thumped a header past Marshall after McCormack had volleyed the ball across goal.
Then Hammell picked out McDonald in the area, and the little striker glanced the ball past the keeper.
The home side came within inches of taking the lead, but Jim Paterson's low drive came back off the post with Marshall beaten.
Stephen Craigan passed up a glorious opportunity to put Motherwell ahead with 13 minutes left, heading over from six yards out.
A couple of minutes later, Varga headed straight at Marshall at the other end.
Incredibly Motherwell did take the lead in the 84th minute. Hartson misjudged the flight of the ball on the edge of his own box, allowing Hamilton to cut the ball back to Kinniburgh who headed into the top corner.
But in the closing moments, Hartson flicked a long ball into the path of Beattie who managed to knock the ball past Marshall and into the net.
Motherwell: Marshall, Paul Quinn, Kinniburgh, Craigan, Hammell, McCormack (Fagan 70), Leitch (Kerr 9), O'Donnell, Paterson, McDonald (Wright 86), Hamilton.
Subs Not Used: Graeme Smith, Keogh, Fitzpatrick, Darren Lee Smith.
Booked: Hammell, McDonald.
Goals: Kerr 20, Hamilton 58, McDonald 60, Kinniburgh 84.
Celtic: Marshall, Telfer, Varga, McManus, Camara, McGeady (Beattie 68), Lennon, Petrov, Thompson, Maloney, Hartson.
Subs Not Used: Boruc, Balde, Aliadiere, Wallace, Lawson, Gardyne.
Booked: Varga, McManus.
Goals: Hartson 14, 32, 44 pen, Beattie 90.
Ref: M McCurry