There had been little time for Leinster to recuperate after their Heineken Cup quarter-final loss at Toulon, and they came up just short against a home side who knew defeat would have effectively ended their own post-season aspirations.
Leinster remain top of the RaboDirectPro12 table despite defeat, and the bonus-point secured here may yet prove crucial in the battle withUlster and Munster for home semi-final advantage.
On a night where Leinster often fell foul of Italian referee Marius Mitrea, Wales international Biggar was their tormentor in chief, kicking five penalties, a drop goal and converting Jeff Hasler’s first-half try.
Cian Healy got Leinster’s try, with Jimmy Gopperth adding the extras and four penalties of his own as the visitors at least left with the consolation of a bonus-point.
Leinster coach Matt O’Connor refused to criticise the referee for the high penalty tally against his side, although he plans to look back at the video.
“We knew it was a tough turnaround in five days with two away matches, and to take a point can be important for us in the run-in. There was a lot of effort and character out there, but unfortunately we weren’t quite good enough.
“It is tough now, we have three games we need to get maximum points out of to make sure we control where we are and from that end it is going to be very tight.
“We have Treviso, Ulster and Edinburgh. They are good sides so we will have to make sure we are on form, have a handful of bodies back and get maximum points.”
It had all started so well for a Leinster side including eight of those who had featured in France, with Gopperth giving them the lead, having already struck the post with a previous penalty attempt, during a bright opening from the visitors.
But the momentum began to shift away from them as they conceded a slew of penalties, three of which were kickable, two of which Biggar stuck between the posts for the Ospreys to lead at the end of the first quarter.
The Welsh side moved the Leinster defence around, with the footwork of number eight Dan Baker particularly impressive, and gaps started to appear.
It took an excellent covering tackle from Rob Kearney to deny Hassler in the corner, but there was no reprieve a few minutes later as Biggar and Richard Fussell combined to send the wing in at the corner, with Biggar adding a majestic touchline conversion.
But Leinster showed their champion class by responding with authority. Possession was reclaimed at the restart and two kickable penalties were rejected in favour of the driving line-out. The first was repelled, the second saw Healy crash over and Gopperth convert.
Leinster trailed by three at the break but undid their good work as ill-discipline allowed Biggar to put the Ospreys nine points to the good.
Leinster were not done, with Healy and Jamie Heaslip making big yardage with some punishing carries to set up a penalty chance for Gopperth. The ex-Newcastle man succeeded but was left with his head in his hands when Dave Kearney failed to hold his looping pass with the line beckoning.
The Ospreys started to look nervy and that anxiety led to them conceding two more penalty chances, accepted with alacrity by Gopperth to tie the scores.
But Biggar stepped up to take control of proceedings.
Having received the ball with defenders closing in on the edge of the Leinster 22, he got away an opportunist drop goal to put the Welsh side back in front with nine minutes to play, and he finished the job with his fifth and final penalty three minutes from time.
Ospreys scorers: Tries: Hassler. Cons: Biggar. Pens: Biggar 5. Drop Goals: Biggar.
OSPREYS: Fussell, Hassler, Spratt, Beck, Natoga, Biggar, Habberfield, D. Jones, Baldwin, Jarvis, R. Jones, A. Jones, Bearman, Tipuric, Baker.
Replacements: H. Dirksen for Natoga (52), N. Smith for D. Jones (61), A. Jones for Jarvis (61), King for Bearman (61), Allen for Baker (75).
Leinster scorers: Tries: Healy. Cons: Gopperth. Pens: Gopperth 4.
LEINSTER: R. Kearney, Kirchner, D’Arcy, Reid, D. Kearney, Gopperth, Boss, Healy, Cronin, Moore, Cullen, McCarthy, McLaughlin, Jennings, J. Heaslip.
Replacements: O’Shea for D’Arcy (71), Fanning for D. Kearney (75), L. McGrath for Boss (75), Ross for Moore (60), Toner for Cullen (64), Murphy for McLaughlin (41).
Refere: Marius Mitrea (Italy).
RaboDirect PRO12: Edinburgh 22 Cardiff Blues 29
Aviva Premiership Rugby: Sale 12 Harlequins 27