Fly-half Biggar scored 14 points with a 100 per cent kicking record in Saturday's 19-14 win with Webb pulling the strings at scrum-half to be named man of the match.
The Welsh international team-mates have led their side to the top of the PRO12 table with four consecutive wins in as many games, including their first triumph in Limerick since 2011.
And Biggar is confident the form of his number nine should ensure both he and his team are able to maintain their own performances in the coming weeks.
"Rhys deserves every bit of credit he's getting," he said. "It's a pleasure to play behind him at the minute - he's absolutely on fire and for us to form a bit of a partnership it makes life a lot easier.
"It's a young squad we've got, we're making no excuses about that, but the way they toughed it out - for us just to come away with a win is what pleases us most.
"We're four from four and that's a big start for us to build on, so who knows what we can go on and achieve this year now.
"Obviously we're grabbing a few headlines for scoring a lot of tries but we know we have to take that with a pinch of salt.
"We know that the hard work comes at places like Thomond Park, this is what you earn your money for."
Click here for the best images from Ospreys' victory over Munster
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