It was just the result the Ospreys needed ahead of their Heineken Cup clashes with Munster over the next two weekends and Scott Johnson used the game to re-introduce a number of his Wales internationals into the side.
The home side were 22-9 ahead at the break, with 21-year-old Tipuric's debut try in the Magners League being the highlight of an otherwise kicking battle between Biggar and his opposite number David Blair and Chris Paterson.
The Edinburgh defence held firm for much of the second half, but with centre Alex Grove in the sin-bin they ran out of numbers on the right as Mike Phillips and Barry Davies combined to send Fussell diving over.
Biggar added a penalty and a long range drop goal to make victory complete and give the Ospreys the boost they needed before travelling to Thomond Park this weekend.
Cardiff Blues picked up a bonus point in Limerick as they fell to a 16-9 defeat in a hard fought game that ended in thick fog. Three Dan Parks penalties kept the Blues in touch throughout a game in which the Blues pack held the upper hand for large periods.
Tom Shanklin actually got over the line in the second half, but when he tried to put the ball down it bounced off the knee of the covering Mick O'Driscoll.
There were other opportunities for the visitors, but a try from experienced flanker Alan Quinlan sealed the victory for table-topping Munster, who are now four points clear of the Scarlets at the top.