The defeat left champions Juve in third place, 10 points behind leaders Inter Milan with 11 games remaining.
Benevento's survival hopes were boosted as they moved seven points clear of the relegation zone in 16th position.
"We are overjoyed. We are a humble team and when we find courage we are hard to beat, we make the opposition play badly."
Andrea Pirlo's Juve were unbeaten in their previous five league games but he could not prevail over his former AC Milan teammate Filippo Inzaghi in the opposing dugout, despite the hosts mustering nine shots on target to Benevento's one.
Juve started on the front foot as Cristiano Ronaldo flashed a shot wide and Montipo denied Alvaro Morata with a diving save.
The referee awarded Juve a penalty for handball but overturned the decision following a VAR review, and Ronaldo found the net only to be denied by the offside flag.
Ronaldo, who scored a hat trick against Cagliari in his last game, was hungry for a goal and stung Montipo's palms before volleying an effort narrowly wide on the turn.
But a catastrophic mistake from Arthur gifted the patient visitors the lead, as his slack pass across his own penalty box was intercepted by Gaich, who finished into the bottom corner.
Ronaldo was Juve's biggest threat as they pushed for a late equaliser, but he could not beat Montipo. The goalkeeper stuck out a leg to deny one effort before parrying another which fell into the path of Danilo but the defender blasted the rebound over.