Hame Faiva scored a hat-trick for Benetton with Ian Keatley adding seven points from the kicking tee as they fell just short.
And the hosts took full advantage with Phillips powering over from short range after a well-worked driving lineout by the Ospreys. Myler added the extras from the touchline to give the hosts a 7-0 lead after five minutes.
After a period of sustained pressure, former New Zealand Under-20s international Faiva smashed his way over the line for Benetton’s first try with Keatley converting.
The Ospreys took a 10-7 lead into the interval after Myler was successful with a penalty kick from 40 metres on the stroke of half-time.
Benetton lay siege to the Ospreys’ try line in the opening stages of the second half as they attempted to maul their way over the line.
The hosts were forced to illegally sack a driving lineout which resulted in blindside flanker Will Griffiths being sent to the sin bin.
And Benetton made the most of their numerical advantage with Faiva touching down for his second try from short range.
Keatley missed the conversion but he made amends with a simple penalty from right in front of the posts soon after as Ospreys full-back Mat Protheroe was penalised for holding on.
The Ospreys were forced to play the final 30 minutes with 14 men when number eight Gareth Evans was given a red card after his shoulder made direct contact with the head of Benetton prop Cherif Traore.
Benetton moved into a 22-10 lead with 22 minutes to go.
Right-wing Iliesa Ratuva Tavuyara chipped the ball over the top of the Ospreys defence before regathering and was brought down just short of the line by North.
After a series of forward carries, Faiva completed his hat-trick as he burrowed his way over the line and Keatley was successful with a touchline conversion.
But the Ospreys made the match a one-score game in the final 10 minutes when replacement scrum-half Venter crossed over following a powerful break from inside centre Kieran Williams with Myler converting.
Benetton prop Filippo Alongi was sent to the sin bin for a no-arms tackle and the home side took advantage as they went to the corner with replacement hooker Lake levelling the scores with a try off the back of a driving lineout.
Myler was successful with the conversion to secure a dramatic victory for the Ospreys.
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