Having made a slow start to the GUINNESS PRO12 season, the Welsh side were desperate to use Europe as a springboard to get their campaign back on track.
They certainly did that, recording a 25-13 win over the Premiership high flyers as Biggar kicked 20 points before Josh Matavesi's late intercept try denied the visitors even a losing bonus point.
The Ospreys now have a daunting trip to Clermont next up, but Biggar, who was making his third Ospreys appearance of the season after returning from the World Cup, insists the Welsh side mean business in Europe.
"This is probably the best win I have had in an Ospreys' jersey," Biggar said.
"We had not made the best of starts to the season and we were up against a very strong side but we are determined to do well in Europe this season after a few poor years in the group stage and this was a good start."
With the tragic events in Paris, there were a number of games called off this weekend, with both Ulster and Glasgow having to wait a week to kick off their campaigns. The Warriors had been due to play in Paris at Racing 92 but thankfully were based out of harm's way just to the north of the city.
The only all GUINNESS PRO12 clash of the weekend went Munster's way and they even secured a crucial bonus point thanks to Simon Zebo's late try against Treviso.
In difficult conditions at Thomond Park, the hosts eventually emerged 32-7 winners, with tries from BJ Botha, CJ Stander and Duncan Casey before Zebo's effort five minutes from time.
Those five points will be invaluable come the end of the group stages, and given the strong winds and heavy rain, skipper Stander was delighted with the start.
"I thought we played well into the wind," the South African said. "It was one of those games were the rain comes straight at you. There were a few kicks that almost went backwards.
"I just tried to lead the boys. They inspire me every week, we're a band of brothers and we play the game to enjoy it. I'm enjoying captaining Munster, it's a big honour and I'm very proud of it."
While the Ospreys and Munster got off to winning starts it wasn't as good a weekend for the Scarlets, who had to settle for a losing bonus point at Northampton.
The Welsh region, who have made a flying start to the GUINNESS PRO12, had their chances at Franklin's Gardens, but couldn't capitalise on two sin-bin periods and eventually went down 15-11.
Still, that result keeps them very much in contention for a quarter-final spot. Leinster, on the other hand, made a disappointing start to the competition as they went down to an impressive Wasps team 33-6 on home soil.
Despite dominating both possession and territory, Leinster lacked the cutting edge to get over the line, and now must win their next clash at Bath.
It was a good weekend for GUINNESS PRO12 clubs in the Challenge Cup, with four wins from five including maximum points for Connacht in the freezing cold in Russia.
Taking on Enisei STM in Krasnoyarsk, leaders Connacht had to cope not only with their opposition but also with the temperatures that dropped below -20 for much of the game.
After a tight first half, the visitors were able to pull away in the second, as tries from Niyi Adeolokun, John Muldoon, Darragh Leader and Rory Parata earned them all five points.
Meanwhile in Pool 2 the Dragons made a flying start at they comfortably beat Sale 30-12, wrapping up a bonus-point success with tries from Ollie Griffiths, Rynard Landman, Adam Hughes and Matthew Screech.
Cardiff Blues ran in seven tries in a routine win over Calvisano, including a score for Lloyd Williams on his 100th appearance for the club.
Edinburgh also impressed as they built on their good start to the domestic season with a 28-10 win over Grenoble thanks to two Cornell du Preez tries, while Zebre went down to last year's champions Gloucester at Kingsholm, 23-10.
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