Thompson was on the verge of being taken off in the 75th minute for an abject display when he volleyed Celtic in front. He then scored again in injury time but he, and Celtic, will need to be more convincing this Saturday when they meet Rangers in the first Old Firm derby of the League season.
Yet, Celtic could easily have heaped pressure upon Falkirk if they had scored from one of several early chances.
Maciej Zurawski has a CV that includes a World Cup goal against England but the Polish striker has failed to justify his £2.2m fee since arriving last month. Zurawski must have thought he had broken his duck when he met John Hartson's knockdown and produced a right-foot volley that goalkeeper Matt Glennon pushed wide.
Paul Telfer came even closer, showing good skill to flick up Craig Ireland's clearance from Thompson's corner before executing a volley that Glennon touched over.
Falkirk were in no mood to go the way of most newly-promoted sides and go down in a blaze of naive attacking principles. The impressive organisation of John Hughes was dutifully carried out by his players, who gradually denied Celtic space and watched as their frustrated hosts began to suffer from their static display.
The mood inside Parkhead was not helped when Falkirk went ahead five minutes before the interval. Neil Lennon appeared to have been fouled in midfield by Craig McPherson but none was given and Falkirk midfielder, John O'Neill, seized on the loose ball and threaded a fine pass into the run of Darryl Duffy, who was barged in the back by Mo Camara as he advanced on goal. Duffy dusted himself down and duly stroked his penalty past Artur Boruc to the joy of the travelling support.
However, Hartson restored parity, and Parkhead's equilibrium, with his sixth goal of the season just four minutes into the second half. Celtic's patient build-up was rewarded as they switched play from right to left, with Thompson picking out Shunsuke Nakamura, who skipped past the tackle of Andy Lawrie before crossing to the back post where Hartson planted a downward header beyond the reach of Glennon.
Strachan's own patience with Zurawski ran out after the hour and Shaun Maloney was invited to join Hartson up front, but it was Thompson who became the hero with 15 minutes left when he put Celtic in front. Stilian Petrov's cross sought out Hartson's head and from the Welshman's knockdown, Thompson conjured up a venemous left- foot volley from 25 yards that flew into the roof of the net.
Thompson ran to the dugout, cupping a hand to his ear in a gesture to the fans who had voiced their frustration of him, only to be rebuked by Strachan who told the midfielder that he had been about to be substituted.
Strachan told the fourth official to put away the substitute board and Thompson gratefully scored again, curling in a fine 20-yard free kick after Petrov had been brought down by Tiago Rodrigues.Reuse content