The Ospreys suffered a major setback in the race for the RaboDirect PRO12 play-off places after they lost 30-27 against Zebre in Parma on Thursday.
Giovanbattista Venditti's try and eleven points from the boot of Luciano Orquera took the Italian outfit into a 16-6 half-time lead.
Dan Biggar responded for the Welsh region with two penalties before the interval, but they were disappointing in the first period.
However, things immediately improved in the second 40 when Justin Tipuric touched down before Ashley Beck went over to take them into the lead.
Alun-Wyn Jones' score looked to have secured the win, but Brendon Leonard and Palazzani crossed the whitewash late on for a dramatic turnaround.
The visitors went into the game with a chance of the top-four - despite going into the match five points behind Ulster immediately above them - but they needed a victory over the minnows.
However, against a side that have struggled for the majority of the campaign, Steve Tandy's men couldn't find their fluency and it was the hosts that went ahead early on.
Orquera had already missed an effort from the tee before the fly-half opened the scoring via a penalty after nine minutes.
Venditti then touched down for a try, which the Zebre pivot converted, as they established a 10-0 advantage.
Although the Ospreys gradually grew into the encounter, reducing the deficit through successive Biggar three-pointers, two more successful kicks from Orquera took the home team into a 16-6 lead at the break.
Tandy needed a response from his squad and he duly received it just a minute into the second period when a Dan Baker surge resulted in Tipuric going over.
The 2012 PRO12 champions were now on the front foot and the comeback was seemingly completed as Andrew Bishop broke through the middle and off-loaded to Beck who crossed the whitewash.
Jones went over for the visitors' third try to give them some breathing space, but Zebre mounted a late response as Leonard's touchdown and Palazzani's last minute score snatched a dramatic win.
Tries: Venditti, Leonard, Palazzani
Con: Orquera, Iannone 2
Pen: Orquera 3
Tries: Tipuric, Beck, AW Jones
Con: Biggar 3
Pen: Biggar 2
Zebre: 15 David Odiete, 14 Dion Berryman, 13 Kameli Ratuvou, 12 Gonzalo Garcia, 11 Giovanbattista Venditti, 10 Luciano Orquera, 9 Brendon Leonard, 8 Samuela Vunisa, 7 Andries van Schalkwyk, 6 Mauro Bergamasco, 5 Marco Bortolami (c), 4 Quintin Geldenhuys, 3 Dario Chistolini, 2 Davide Giazzon, 1 Salvatore Perugini.
Replacements: 16 Andrea Manici, 17 Matias Aguero, 18 Dave Ryan 19 George Biagi, 20 Filippo Ferrarini, 21 Guglielmo Palazzini, 22 Tommaso Iannone, 23 Ruggero Trevisan.
Ospreys: 15 Sam Davies, 14 Hanno Dirksen, 13 Ashley Beck, 12 Andrew Bishop, 11 Aisea Natoga, 10 Dan Biggar, 9 Tom Habberfield, 8 Dan Baker, 7 Justin Tipuric, 6 James King, 5 Alun Wyn Jones (c), 4 Ian Evans, 3 Aaron Jarvis, 2 Scott Baldwin, 1 Nicky Smith.
Replacements: 16 Scott Otten, 17 Marc Thomas, 18 Adam Jones, 19 Ryan Jones, 20 Joe Bearman, 21 Sam Lewis, 22 Tito Tebaldi, 23 Jeff Hassler.
Venue: Stadio XXV Aprile, Parma
Referee: Peter Fitzgibbon (Ireland)
Assistant Referees: Elia Rizzo (Italy), Filippo Bertelli (Italy)
TMO: Carlo Damasco (Italy)