Zebre had not won in 10 games but five tries and fly-half Carlo Canna's 22 points secured a bonus-point victory.
Two second half tries from Rynard Landman and one from Wales wing Hallam Amos were not enough for Kingsley Jones' side.
Dragons finish the Pro 12 season as the lowest placed Welsh region.
Angus O'Brien's penalty had given Dragons an early lead but Zebre replied through tries from Andrea Lovotti and Kayle van Zyle.
Replacement Landman crossed early in the second half to give Dragons hope.
But tries from Leonardo Sarto, Bruno Postiglioni and Kelly Haimona saw Zebre extend their lead.
Landman and Amos added further tries for the visitors, who finish 11th the Pro 12 with only Zebre and Treviso below them in the table.
Zebre's victory saw them move off the bottom and leapfrog Treviso to secure a Champions Cup spot for next season.
Zebre: Ulrich Beyers; Kayle Van Zyl, Tommaso Boni, Matteo Pratichetti, Leonardo Sarto; Carlo Canna, Guglielmo Palazzani; Andrea Lovotti, Oliviero Fabiani, Guillermo Roan, Quintin Geldenhuys (capt), Marco Bortolami, Filippo Cristiano, Andries Van Schalkwyk.
Replacements: Bruno Postiglioni, Andrea De Marchi, Dario Chistolini, Gideon Koegelenberg, Federico Ruzza, Luke Burgess, Kelly Haimona, Mils Muliaina.
Dragons: Rhys Jones; Adam Hughes, Adam Warren, Jack Dixon, Hallam Amos; Angus O'Brien, Charlie Davies; Phil Price, Rhys Buckley, Lloyd Fairbrother, Matthew Screech, Nick Crosswell (capt), James, Benjamin, James Thomas, Ed Jackson.
Replacements: Elliott Dee, Luke Garrett, Shaun Knight, Rynard Landman, Harri Keddie, Saral Pretorius, Dorian Jones, Carl Meyer.
Referee: David Wilkinson (IRFU)
Assistant referees: Elia Rizzo, Simone Boaretto (FIR)
Citing commissioner: Achille Reali (FIR)
TMO: Stefano Marrama (FIR)
Newport Gwent Dragons suffered their 10th consecutive Pro 12 defeat as Zebre qualified for next season's European Champions Cup.