The Ospreys secured their second bonus point victory with fly half Dan Bigger among the tryscorers en route to reaching 1,000 points for the league, just the second player in history to do so.
The Welsh side scored three tries in each half with Italy scrum half Tito Tebaldi producing a man of the match behind the powerful Ospreys pack with another impressive display.
Full-back Richard Fussell, wings Eli Walker and Jeff Hasler, Tebaldi and captain Alun Wyn Jones all crossed for tries for the Ospreys with wing Danie Poolman and centre Eion Griffin replying for the home side.
Craig Ronaldson kept Connacht in touch with his boot to leave the home side trailing 22-12 at half-time but the Ospreys finishing power proved too hot to handle for the home side who gave their usual gutsy display at home but the superior class of the visitors told in the end.
