Ross McCann got Edinburgh level when it looked like the returning Emiliano Boffelli had hesitated too long with his pass, but the winger skipped back inside and boshed off a few defenders to score.
Zebre did not let up and crossed the line again as scrum-half Gonzalo Garcia sniped from the base of a ruck to dive over.
The visitors rightfully led at half-time and went further ahead when Giacomo Da Re knocked a penalty over to give Zebre a 10-point lead.
Edinburgh are known for being stronger in the second-half and they gave themselves hope when Ali Price zipped the ball to Mosese Tuipulotu and he crashed over for his first league score.
With the conversion added, it became a three-point game, but Zebre responded brilliantly and replacement Tommaso di Bartolomeo gladly fell over the line from the back of a rumbling maul.
Edinburgh put the pressure on, with Prisciantelli seeing yellow before Luke Crosbie crashed over from short range.
Guido Volpi was then sent off for a high shot on the Edinburgh captain and it seemed Sean Everitt’s side would make their numbers count.
However, an unbelievable defensive effort from Zebre kept the hosts out and they held on for one of the most famous victories in their history.
Edinburgh: Goosen, Boffelli, Currie, Tuipulotu, McCann; Thompson, Price; Venter, Harrison, Rae, Sykes, Young, Crosbie, Watson, Currie.
Replacements: Morris, Hislop, Hill, Skinner, McConnell, Vellacott, Healy, Lang.
Zebre: Prisciantelli, Trulla, Paea, Mazza, Gregory; Da Re, Garcia; Buonfiglio, Bigi, Hasa, Canali, Krumov, Andreani, Stavile, Licata.
Replacements: Di Bartolomeo, Rizzoli, Pitinari, Volpi, Ferrari, Fusco, Montemauri, Morisi.
