The Japanese international's perfectly-struck set-piece with only nine minutes remaining ensured the Scottish champions emerged from the competition's group stages for the first time.

Celtic's 1-0 win, coupled with their 3-2 defeat against United at Old Trafford, means that even if Benfica win their last game against the English side, the Glasgow club go through on goal difference ahead of Sir Alex Ferguson's team.

Celtic keeper Artur Boruc was also a hero for the Hoops, saving a Louis Saha penalty in the final minute after Spanish referee Manuel Enrique Gonzalez ruled that a Ronaldo free-kick had struck the hand of Shaun Maloney.

Celtic skipper Neil Lennon had to be told they had qualified for the knockout phase, but the northern Irishman was quick to condemn the penalty decision before pouring praise on Boruc and Nakamura.

"It's the best result of my career," said Lennon. "The (penalty) decision was crazy but credit to Boruc for the save.

"If this means we go through, then I am ecstatic."

He added: "Nakamura has to be one of the best free-kick takers in the world. You've seen that he did exactly the same against United at Old Trafford."

Celtic manager Gordon Strachan and his Manchester United opposite number Sir Alex Ferguson were in shock for different reasons.

"I can't believe it, I will have to double check in the morning just to make sure," said Strachan, who has enjoyed frosty relations with Ferguson since writing a tell all book about the United chief, having played for him both at Aberdeen and United.

Strachan went on to praise Nakamura.

"He is as good as anyone in the world right now."

Ferguson admitted that his side had failed to take advantage of all their dominance.

"To be honest, losing this game is very hard to take," he said.

"I am in shock," was his succinct assessment.

It means United will now fight it out with Benfica for the remaining qualifying spot in Group F.

United had pushed Celtic on to the back foot from kick-off as they looked to win the group with a game to spare.

French striker Saha tested Boruc in the fourth minute when he latched on to Paul Telfer's loose ball and struck a low drive from 20-yards which the Polish international gathered to his chest.

An audacious Wayne Rooney volley from a Ryan Giggs corner whistled just wide of the post in the 30th minute with Boruc struggling to get across his line.

Strachan was clearly displeased with his side's first half performance and made a double substitution at the break, bringing Czech international Jiri Jarosik and Shaun Maloney on in place of Polish striker Maciej Zurawski and Dutch midfielder Evander Sno.

The switch seemed to have the desired effect and Celtic took the upper hand in the opening stages of the first-half.

In the 53rd minute a poor kick-out from United goalkeeper Edwin Van Der Sar found its way to Nakamura. The Japanese playmaker played the ball to Danish midfielder Thomas Gravesen whose shot from 20-yards required the Dutch international stopper to dive low to his right to save.

This promising period for Celtic did'nt last and United soon took command.

In the final quarter hour both sides were evenly matched.

United's Portuguese international Cristiano Ronaldo tried to take matters into his own hands with a mesmerising run in the 78th minute which concluded with a shot from 18 yards but which deflected off the foot of Lee Naylor and flew just wide of the post with Boruc at full-stretch.

With 10 minutes remaining Celtic were awarded a free-kick 35-yards from goal when United defender Nemanja Vidic fouled Jarosik.

Nakamura, who had scored from a set-piece from a similar position against United at Old Trafford, stepped up and curled a perfect left-foot shot which looped over the wall and into the top corner of the net.

United threw everything at Celtic to try and salvage the point they needed to qualify and with a minute remaining they were awarded a penalty when Ronaldo's free-kick struck the hand of Maloney.

Saha took the kick and hit a powerful right-foot effort towards the left-hand corner only for Boruc to throw himself to his right and palm the way.

Ferguson refused to lay the blame at Saha's door.

"Louis is obviously disappointed to miss the penalty but the players will help to lift him because we are all together at this club.

"There are no problems with the boy. I am sure he will miss another penalty in his career at some point."