Henson supplied five penalties, two conversions and a second-half try in a superb all-round display.
The 23-year-old Wales star also kicked immaculately out of hand.
Edinburgh were determined to gatecrash the party and claimed deserved tries through hooker Andrew Kelly and replacement prop Alasdair Dickinson.
Needing two points to lift the title, the Ospreys found the Scots a handful and had to fall back on boot of Henson to guide them home.
It was 19-7 to the hosts at the break but Edinburgh had contested every inch of territory.
Even though Henson settled the home nerves with a quick-fire penalty treble, the Scots posed all kinds of problems with their aggression up front and ambition behind.
But it was the Ospreys who claimed the first try. From a scrum some 35 metres out, Wales back-row forward Ryan Jones broke and found Steve Tandy, who sent Jason Spice speeding across.
But the score far from discouraged the visitors. They attacked hard down the left and found a chink in the Ospreys' armour when hooker Andrew Kelly forced his way through weak tackling.
Henson slotted another penalty, but home coach Jones would hardly have been happy with the way his side performed.
Edinburgh cut the deficit to 10 points when Dickinson went outside Price, but the Ospreys soon hit back.
A rare flowing move from the hosts, set up by a strong run in midfield from Ryan Jones, ended with Henson gliding over.