The Glasgow giants had to come back from a goal down to secure the points after Darryl Duffy had fired Falkirk into a shock 39th-minute lead from the penalty spot after Mo Camara had felled the Scotland Under-21 international.

But John Hartson levelled after the break with his sixth goal of the season before Thompson let fly with a breathtaking volley moments after Hoops’ boss Gordon Strachan decided against substituting the former Bolton man.

Thompson completed his brace in injury time with a thunderous left-footed free-kick which flew into the top corner.

However, after being thumped 8-1 in the CIS Insurance Cup on their last visit to Celtic Park a year ago, Falkirk were encouraged by the home side’s uninspiring start to the game.

Camara twice wasted good chances to put the ball into the danger area early on, but Maciej Zurawski finally brought the crowd to life in the 11th minute.

The ball fell kindly to the Pole outside the area and he sent a right-foot shot towards goal which Matt Glennon comfortably saved.

But the Bairns’ goalkeeper bettered that stop moments later when he flung himself to his right to tip Paul Telfer’s dipping effort over the top after Celtic’s first real spell of pressure.

Stilian Petrov then tested Glennon, but he easily saved before Bobo Balde endeared himself to the home support with a full-blooded double tackle on Duffy.

But Celtic struggled to find their recent fluency, when they swept aside Dundee United and Artmedia Bratislava.

The Bell’s First Division champions were concentrating on John Hartson, but Tiago Rodrigues was too focussed on the task and was the first man to go into Alan Freeland’s book.

The visitors were presented with the perfect chance to grab a shock lead in the 39th minute when Steven Thomson went down under the challenge of Camara.

Scotland Under-21 international Duffy picked himself up and coolly sent Artur Boruc the wrong way.

Even though Nakamura did not look fit, he supplied a special delivery for Hartson to equalise just four minutes after the restart.

The Japanese midfielder swung an inviting ball to the back post and the Welsh international barely had to do anything to head the ball past Glennon.

There were gaping spaces in the Celtic defence and Duffy should have exploited that in the 59th minute, but chose to bring the ball back on his left foot and fired wide.

Strachan did decide to bring on Maloney moments later for Zurawski to inject more energy into the Celtic side.

Falkirk head coach John Hughes responded by introducing Alan Gow for Daniel McBreen in the 65th minute.

Thompson was having a bad day and foolishly earned himself a yellow card in the 71st minute when he refused to leave the field after having treatment for a head knock.

Falkirk sat deeper and it needed something special to break them down, but Thompson answered the call with a stunning strike in the 75th minute.

Hartson knocked the ball down to him just outside the area and he struck a sweet volley past the despairing dive of Glennon and into the top corner of the net just minutes after Strachan considered withdrawing him.

Craig Beattie had been waiting to come on but Strachan told the youngster to sit down again.

Maloney tried the spectacular moments later but Glennon held his curling effort before Nakamura blazed over from long range.

That was the Japanese start’s last contribution as Beattie replaced him with 10 minutes left.

But, in the first minute of injury time, Thompson hit the back of the net again with a curling free-kick from the corner of the penalty area.