However the Italian outfit came out fighting after the interval and Luca Redolfini's try and a conversion and another penalty from Halangahu reduced the Ospreys lead to just the solitary score.
But the Welsh outfit were able to the weather the pressure and a late rally from Biggar - who slotted two further penalties and converted his own try seven minutes from time - sealed the win.
Forwards coach Humphreys was encouraged by the response of his team to Zebre's fight and wants to see more of it as the Ospreys face Treviso next and then Leicester in the start of the Heineken Cup campaign.
"Zebre had their tails up and came back to just the one score but the response from us was excellent, we showed good composure to pull ahead again," Humphreys told the official Ospreys website.
"When it got so tight we could have panicked but instead the boys were disciplined and went back to the procedures we work on all week long and knew their responsibilities.
"We were professional in our approach and that allowed us to get the job done. We've now got two massive games coming up. We will need to be at our very best if we want to get off to a winning start. "It's important that we get a good crowd behind us and that they are patient and stay with us if things don't go our way. That's what every team needs if they want to make a mark in Europe.
"We've said all along since the summer that we wanted to be building momentum as we came into October and the Heineken Cup and that's exactly what we've done. Hopefully now we can do ourselves justice these next two weeks."
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