Henrik Larsson, Didier Agathe, Stilian Petrov and Chris Sutton provided the goals that allow the Hoops to head into the second leg of the third round qualifier at Parkhead with a great opportunity to progress in the competition.

The signs had not looked too promising for Celtic heading into this game - they were dealt a blow before the tie with the news that Johan Mjallby’s knee injury meant he could not take part.

He picked up the knock in last Saturday’s SPL opener against Dunfermline – a game which saw Celtic fail to find the back of the net for the first time in league competition since December 2001 – as they produced a jaded looking performance.

But the hunger which saw them progress to the final of the UEFA Cup last year was back in Budapest tonight and Martin O’Neill’s men quickly set about trying to find the away goal that he so desperately craved ahead of the return leg at Parkhead.

MTK had looked strong to begin with, with striker Welton Santos looking dangerous for the home side, but the difference between the two teams in the first half was that they failed to take their chances whereas Celtic were far more deadly with their finishing.

Larsson had already equalled the record held by Ian Rush and Peter Lorimer for the most European goals scored for a British club and he made the record his own when he fired home his 31st tonight.

With 16 minutes on the clock, the prolific Swede met a Paul Lambert header and Roland Juhasz and Oliver Pusztai both failed to clear the danger, allowing the Hoops striker to lob goalkeeper Zoltan Vegh and hand Celtic the lead.

O’Neill’s joy at Larsson’s opener quickly turned to physical pain when he leaped off his seat to celebrate and smacked his head on the roof of the dug-out.

Some treatment from the Celtic doctor was required but O’Neill’s attention quickly returned to the action on the field.

Agathe had been quoted in France Football recently saying that the Bank of Scotland Premier League no longer excited him and that only European nights held any interest for him now.

And he showed plenty of interest in tonight’s tie when he joined Larsson on the scoresheet.

A Stilian Petrov ball into the path of Chris Sutton allowed the striker to produce an impressive shot only for the effort to be parried by Vegh. But his clearance only got as far as the feet of Agathe and all that was required of the pacy winger was to tap home from six yards out.

Neither manager opted to make any changes during the half-time interval and MTK quickly set about trying to reduce the deficit once the second half was underway.

Gabor Zavadszky tried his luck with a long, low effort just a few minutes after the re-start but Douglas comfortably managed to scoop the ball to safety, much to the disappointment of the home crowd.

Celtic were still hungry for more goals and they were unlucky not to add to their lead when Petrov curled the ball into the box, meeting Varga at the back post, only for the defender to sent the effort just wide of target.

The game was halted for a couple of minutes when a fault in the sprinkler system led to a fountain of water spurting all over the pitch, providing a moment’s respite for both sets of players in the smouldering heat of the Ferenc Puskas Stadion.

When the game restarted, MTK continued to try to push forward and Santos had another chance to net for the Budapest side only to nod just wide of the post under pressure from Joos Valgaeren.

A couple of minutes later the Hungarians were unlucky not to pull a goal back when substitute Sandor Torghelle saw his lopping header smack off the crossbar.

Celtic showed they were not rattled by the close call when they surged up the park and netted their third goal of the night.

Thomson showed great skill to surge into the area from the left wing only for Vegh to block his shot at the near post. The ball fell to Petrov, who rounded Gabor Halmai, before slotting home.

As the game headed towards the last 10 minutes, O’Neill used up all his substitutions – and that decision almost led to another goal.

Momo Sylla had replaced Agathe and he squared the ball across the face of goal to rising star Liam Miller but the young midfielder just failed to connect and the opportunity was lost.

But Celtic saved the best for last when Sutton produced an amazing diving header from a Larsson pass to nod the ball into the back of the net in the final minute of the game – leaving Celtic with the knowledge that progression to the group stages of the Champions League lay firmly in their own hands.