Celtic edged through to the knockout phase of the Champions League thanks to a wonderful Shunsuke Nakamura free-kick and a penalty save from Artur Boruc.
Nakamura was on target for Celtic
The Japanese star curled a sweet 30-yard strike into the top corner after 80 minutes to brighten what had been a cagey affair.
Manchester United striker Louis Saha was guilty of a terrible miss when he appeared to assume he was offside.
And Saha's night got worse when Boruc saved his last-minute penalty kick.
United must now take a point from the final Group F match at home to Benfica to progress in the tournament.
Celtic, who have never made the last 16 in the Champions League, are level on nine points with United.
But Gordon Strachan's side have a better head-to-head record with United, having scored away goals in their 3-2 loss at Old Trafford.
The visitors settled into a neat passing rhythm early on, taking the sting out of a keenly anticipated contest with sustained periods of possession.
Celtic were uncharacteristically timid in their approach, playing with two solid blocks of four and providing nothing for their strikers.
Neither goalkeeper had been threatened until an ambitious 20-yard volley from United's Wayne Rooney skidded narrowly wide on 29 minutes.
A mistake from Bobo Balde then allowed Cristiano Ronaldo to race in on goal but the defender's recovering lunge took the pace off the Portuguese star's shot and Boruc got down smartly to save.
United must now take a point from the final match
Celtic made a rare break forward late in the first half but Thomas Gravesen's header from a Maciej Zurawski cross flashed harmlessly across the goal.
Strachan introduced Jiri Jarosik and Shaun Maloney after the interval but the switch did little to enliven proceedings.
Saha headed wide from a corner and Rio Ferdinand hooked a shot high over the crossbar from a similar situation.
Gravesen and Nakamura delivered shots on target but United keeper Edwin Van der Sar gathered with ease.
Ronaldo did well with a strong run after 77 minutes only to see his angled strike take a slight deflection and fizz wide.
The game burst into life in the final 10 minutes and Nakamura brought the previously subdued home support to their feet with his sensational free kick.
Saha was then guilty of dithering in front of goal, looking over at the linesman and allowing Boruc to block his shot.
United were awarded a penalty when Maloney handled a Ronaldo free-kick, but Boruc flew to his right to push away Saha's spot-kick.
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Celtic: Boruc, Telfer, Balde, McManus, Naylor, Nakamura (Miller 85), Gravesen, Lennon, Sno (Jarosik 46), Vennegoor of Hesselink, Zurawski (Maloney 46).
Subs Not Used: Marshall, Wilson, McGeady, O'Dea.
Booked: McManus, Gravesen, Lennon.
Goals: Nakamura 81.
Man Utd: Van der Sar, Neville, Ferdinand, Vidic, Heinze (Evra 87), Ronaldo, Carrick (O'Shea 87), Scholes, Giggs, Saha, Rooney.
Subs Not Used: Kuszczak, Brown, Richardson, Fletcher, Silvestre.
Ref: Manuel Gonzalez (Spain).