Replacement Guglielmo Palazzani's try right at the death put a big dent in Ospreys' RaboDirect PRO12 top four hopes as Zebre took an entertaining 30-27 victory in Palma.
The Italians had led 16-6 at the break after Giovanbattista Venditti's try plus eight points from Luciano Orquera.
Ospreys hit back immediately after the break, Justin Tupuric with a try after just 34 seconds before Ashley Beck and Alun Wyn Jones seemingly put them on course for a comeback win.
But tries from Brendon Leonard plus Palazzani's effort in the 82
nd minute broke Ospreys hearts, leaving them with just the losing bonus point and four points behind fourth-placed Ulster having played a game more.
Ospreys had started the game looking to make it three RaboDirect PRO12 wins in a row but it was Zebre who had the first chance to open the scoring but Orquera was wide with his penalty.
With conditions perfect for flowing rugby, both sides were setting their stall out early, with Dan Biggar and Hanno Dirksen combining well before the move broke down.
But an error at Ospreys' line out - Scott Baldwin overthrowing the ball - saw Zebre turn over possession and with Beck caught offside, Orquera made no mistake second time round, giving his side the lead after nine minutes.
The Italians were rewarded again for their pressure just three minutes later when Orquera side-stepped his way through Ospreys' defence before feeding a long ball across to wing Venditti to score. Zebre's no.10 adding the extras for 10-0.
Biggar got his side's first points on the board with a penalty on 19 minutes before the Ospreys enjoyed their best move of the game so far a minute later.
A sweeping attack played in full-back Sam Davies but with the try line fast approaching, Zebre centre Kameli Rauvou was back with a desperate ankle tap, although Ospreys did not come away empty handed, with Biggar again sending over his kick.
Orquera extended his side's lead with a second penalty shortly before the half hour mark before Ospreys again tried to make some ground with an attack but Baldwin dropped Biggar's pass.
There was still time to trade penalty attempts in the final minutes of the half, but with Biggar sending his wide, Orquera made no mistake to give his side the 16-6 lead at the break.
Whatever was said to the visitors during half-time appeared to work however as they pulled a try back almost immediately after the restart.
Dan Baker gathered the ball, dodging flanker Andries Van Schalkwyk and breaking free before putting in Tipuric to cross, Biggar with the extras and suddenly Ospreys were right in it at 16-13.
Biggar was proving to be a thorn in Zebre's side and almost set up another try when he ran the ball out of his own 22, but despite Beck and Hanno Dirksen picking up the baton, Zebre eventually cleared.
But they were unable to stop the Welsh side on 54 minutes, as Andrew Bishop cut through Zebre's defence with ease, playing in Biggar who left Beck with a simple score.
Biggar added a second conversion and it was the same result 13 minutes later after Ospreys added a third try, this time via Jones following a line-out.
Ospreys were sniffing the chance of a valuable bonus-point fourth try but they were undone in defence as replacement Tommaso Iannone capitalised to play in Leonard to crash over.
Iannone converted and with yellow cards dished out to both sides, Samuela Vunisa for Zebre and Jones for Ospreys, the game entered the final minutes in the balance before Palazzani stole the headlines.
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