Nothing could separate the two Serbian stars in an opening dominated by serve, until Tipsarevic's gradual growth in confidence and comfort on the controversial blue clay reached a crescendo in the tie-break.
Taking the first four points in succession, Tipsarevic stormed to a 5-1 lead as the two switched ends en route to a 7-2 tie-break win.
Djokovic withered in the second, and his serve was the first to buckle in an error-strewn sixth game which Tipsarevic followed up with an impressive hold to lead 5-2.
Though the top seed was able to escape a triple match point in the following game and pull one back, Tipsarevic marched on to the semi-finals from his first advantage point in the following service game after a thrilling back-and-forth tussle with his compatriot as the pair skidded frantically along the surface.
The straight-sets defeat for Djokovic at the hands of his good friend mean that of the traditional 'big four', only world number three Roger Federer remains in contention for the 2012 title.
Djokovic followed number two Rafael Nadal out of the Madrid Open, and the top-ranked pair have complained bitterly about the slippery nature of the courts at the Masters event.
Djokovic again looked ill at ease as his bid to retain the title he beat Nadal to win in 2011 ended with a whimper.
Nadal was beaten by fellow Spaniard Fernando Verdasco in the third round on Thursday and both he and Djokovic have threatened not to return next year unless the traditional red dirt courts are reinstated.
Tipsarevic, seeded seventh, will battle for a place in the final with Federer, who bea tfifth-seeded David Ferrer of Spain 6-4 6-4.
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