Djokovic and Goffin traded a number of blows, with both players contesting numerous break points, in a match that relentlessly swayed from one end to the other.
Second seed Novak Djokovic fell 6-2, 3-6, 7-5 on Friday to David Goffin at the Monte Carlo Masters to join a growing list of high-profile upset victims.
An early break in the third set saw Djokovic take control but he failed to secure the double break, much to his frustration. Goffin, though, held on to take the game and with it a 2-0 lead. He came back strongly and forced Goffin to concede a break point in his first service game. The 10th-seeded Goffin kept his calm to take the first set 6-2.
It was in controversial circumstances that the Belgian came through as Djokovic was given a time violation by the umpire at deuce, having already saved four match points, and the Serb then went on to lose.
The Belgian had never previously beaten Djokovic in five matches against the former World No 1 - and had won just one set - but held his nerve to reach the semi-finals with a fine 6-2, 3-6, 7-5 win.
Pouille stepped up his game and a cross-court backhand gave him break point, which he took when Cuevas sank a backhand into the net.
The momentum was with Djokovic, but the resilient Goffin had other ideas.
Earlier, Spanish clay-court specialist Albert Ramos-Vinolas followed up his victory over Murray with a 6-2 6-7 (5-7) 6-2 victory against Croatian fifth seed Marin Cilic.
After dumping out world number one Andy Murray in the third round the day before, the diminutive Spaniard returned to knock-out mode as he tamed Cilic to surge into the first Masters 1000 semi-final of his career.
Goffin, who broke into the top 10 for the first time earlier this season, saved two set points while serving at 2-5, which left Djokovic ranting furiously in Serbian but his frustration was short-lived as he served out the second set for 6-3.
Ramos-Vinolas needed 2 1/2 hours to win, but could have got there faster after leading 5-3 in the tiebreaker - only for Cilic to level the set score with a volley that only just landed in.
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