As a result Quins will be looking to become the first team to win every one of their pool games to go on to win the tournament.
And unless French heavyweights Clermont or Toulon, can rack up nine, or five tries respectively away to the Scarlets or Montpellier, Quins will also wrap up the top seed for the quarter-finals.
O'Shea said: "It was a mature performance and we are delighted with the attitude of the players.
"There was a lot of experience out there of playing together and in tough conditions but it was one of those nights when you had to roll the sleeves up and show as a group what it means to play for each other. We had to grind it out.
"We knew the kicking duel would be crucial and Nick Evans, Danny Care and Mike Brown kept us playing in the right areas.
"To come to the south of France and get a win against any team is outstanding, especially given that's only the second time in the Heineken Cup that Biarritz have been beaten here.
"That was the motivation for the players as well as aiming to be number one seeds for the quarter-finals which could be important."
In the other game in the pool Connacht narrowly avoided being Zebre's first victim, with a late penalty and drop goal from Dan Parks helping them to a 25-20 victory.
Biarritz 9 Harlequins 16
Scorers
Biarritz
Penalties: Yachvili 3
Harlequins
Tries: Guest
Conversions: Evans
Penalties: Evans 3
