The Welsh region kept their unbeaten record on Italian soil but they surrendered their 11-match winning run when they salvaged a draw against a well organized and well drilled Benetton Treviso side.
Morgan, who was making his Heineken Cup, saved his side’s blushes with the long-range penalty as it looked like the Italian side would record an historic win.
Tommy Bowe, who overtook Shane Williams to become the Ospreys leading try-scorer in the Heineken Cup, scored one of his side’s two tries but the Italian side will be frustrated they didn’t win a game they led for most of the second half.
The Ospreys lost Wales and Lions prop Adam Jones to injury before kick and Aaron Jarvis, the former Bath tighthead, was drafted into the starting line-up but the visitors soon found themselves 3-0 behind to a Kris Burton penalty.
The Welsh region then took the lead midway through the first half when Ireland and Bowe wing showed impressive strength and strength to crash over for the game’s first try.
Biggar added the conversion but his opposite number Burton kept the hosts in the contest when he slotted over two penalties to claw his side back to within a point to make it 10-9 at half-time.
But the home side came out all guns blazing at the start of the second half and soon crossed for two early tries by prop Michele Rizzo and wing Benjamin De Jager to go back ahead.
The Ospreys replied with another Biggar penalty before second row Ryan Jones latched onto a loose ball at a Treviso lineout to score and claw his side back to within a point at 21-20.
Scrum-half Tobias Botes then crossed for Treviso’s third try to stretch his side’s lead before Biggar, who crossed the 200-point mark for the Ospreys in the Heineken Cup, and Morgan rescued a game the visitors looked like losing.