Thompson's 30-yard strike finally confirmed three points for a Celtic side which had dominated a game which struggled to catch alight thanks to Rangers' unusually negative tactics.
It was clear that the struggling Ibrox side - knocked out of the Champions League qualifier by CSKA Moscow last week - had come to Parkhead to play a defensive game and hoping to snatch the tie on the break.
Nacho Novo was left to chase long balls for most of the game as Celtic dominated possession and territorial advantage.
Celtic's latest signing Juninho proved just why Middelsborough fans didn't want their club to let him go, with a spirited display of classy football and determined tracking-back.
The Brazilian World Cup winner bamboozled the Rangers defence several times, particularly in the first half. Perhaps only his lack of practice alongside his new team-mates prevented him from scoring - when he broke through the defence once, Henri Camara snatched the ball from his feet and blasted wide.
Celtic dominated most of the game, but failed to demonstrate that decisive touch. Chris Sutton's absence through injury may have been the cause as this new-look Celtic side has failed to play a consistent forward line since the beginning of the season.
john Hartson - having hit four goals in Celtic's last two league games - struggled at times to link effectively with his partner Henri Camara. Behind them, Juninho and Petrov looked more likely to score until another midfielder, Thompson, finally broke the deadlock.
Celtic had welcomed back Stan Varga and Jackie McNamara after their recent injuries. Both had comfortable games, as did the entire Celtic team given Rangers' reluctance to break forward.
For the visitors, French centre half Boumsong looked promising and right back Allan Hutton played well, but this Rangers team lacked power, conviction and any kind of magic which might have threatened Celtic. The ineffectual Prso had one shot saved by Marshall, who also blocked an Alex Rae attempt late in the game.
Before the game, spectators were alive with more rumours of signings before the August 31 deadline. there has been talk of new players coming in, including Livingston's David McNamee, an unnamed left sided defender and even Newcastle and former England striker Alan Shearer. for their part, Rangers seem likely to sign the troubled Hakin Yakin, formerly of Basle and PSG, but who has been released by Stuttgart.
The game started brightly with almot all of it played in Rangers' half. The controversial Alex Rae got away with an off-the-ball "straight arm" on Juniho, and Rangers gave away numerous fouls as they seemed determined to play for a draw.
Later, Wallace replaced Camara and Sylla came on for Hartson before Thompson's wonder goal. The ball had broken free from Rangers' penalty area and the England player had time to gather it and unleash a ferocious swerving shot past a lunging Ricksen and despairing Klos.
Game over and first blood to Celtic. Comfortable in the knowledge of a 5-point cushion before the first Champions League game on September 14, when Henrik Larsson and Barcelona come to town. Now there is one team who won't arrive at Parkhead hoping for a draw!
Man of the Match: Neil Lennon.
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