Cecchinato appeared to be cruising as he built a two-set lead with Djokovic battling neck pain. Djokovic, a 12-times major winner, fought back in typical fashion to win the third set but his determined opponent was not done.
Cecchinato held his nerve in a tight fourth set tiebreak to claim a famous victory on his fourth match point. Up next for Cecchinato is Dominic Thiem.
Austrian claycourt specialist Thiem thumped a battle-weary Alexander Zverev 6-4 6-2 6-1 to reach the semi-finals at Roland Garros for the third consecutive year.
US Open champion Sloane Stephens set up a semi-final clash against fellow-American Madison Keys after easing past Russian Daria Kasatkina 6-3 6-1.
Keys, who lost to Stephens in the US Open final at Flushing Meadows last year, rallied from a break down in the opening set to beat Kazakhstan’s Yulia Putintseva 7-6(5) 6-4.