The champions went ahead in the 52nd minute thanks to an own-goal by Jonathan Biabiany, but midtable Parma hit back with 13 minutes to play through Sergio Floccari.
Unai Emery's side opened their campaign with a draw against Lille but were well worth their win at the Mestalla , although they fell behind to a Sergio Floccari goal.
The struggling visitors took a seventh-minute lead through Sergio Floccari but goals later in the first half from Stefano Guberti and Giampaolo Pazzini were enough to give Samp the three points.
Gianni De Biasi's side went into the game having lost five of their last six games following their midweek defeat by Bari and got off to another miserable start as Sergio Floccari put Lazio ahead after 16 minutes.