Tsonga, who was defeated by Djokovic in the final in Melbourne in 2008 and had not advanced past the quarter-finals of a grand slam since, looked down and out after the third set but rallied to beat the Serb after three hours 52 minutes.
It was the second successive five-set victory for the 10th-seeded Frenchman, who until his fourth-round win over Nicolas Almagro on Monday had never played a five-set match before.
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Hide AdTsonga now meets world number one Roger Federer in the semi-finals on Friday.