Dan Biggar claimed an 18-point haul in a six-try Ospreys performance as the power-packed visitors overcame Connacht in the RaboDirect PRO12.
The Wales international fly-half's haul took him to a notable milestone as he went beyond 1,000 career points in the league.
The visiting Welsh region touched down three times in the opening 29 minutes, including an intercept effort from Biggar, with young out-half Craig Ronaldson keeping Connacht in touch at 22-12 down at half-time.
It was a two-point game after Aly Muldowney set up Danie Poolman for Connacht's opening try, but even though Eoin Griffin added a second, replies from Tito Tebaldi, Jeff Hassler and captain Alun Wyn Jones made it a resounding 43-26 winning margin in the end.
Ronaldson was making his first start at this level after a stellar season for Ulster Bank League club Lansdowne, and he settled any early nerves with a fourth-minute penalty.
The 23-year-old missed his second shot at the posts and it was his pass which opposite number Biggar read for his intercept try, the conversion moving the visitors 7-3 clear against the run of play.
The Ospreys, with their strong pack growing in influence, touched down again on the quarter-hour mark.
Ian Evans and the returning Justin Tipuric were both prominent in the build-up, exposing some poor tackling from Connacht, and full-back Richard Fussell provided the finishing touches with Biggar converting.
Steve Tandy's men might have had a third try as second row Evans bounded through once more, however he threw a loose pass to Hassler which the winger knocked on.
Connacht were unable to pressurise the Ospreys try-line and were largely reliant on the left boot of Ronaldson, who tagged on two more place-kicks before he hobbled off to be replaced by Dan Parks, the only player to ever previously reach 1,000 points in the Celtic League.
By half-time the Ospreys had run in a third try through Eli Walker, who made it over in the corner following a pacy break, and Biggar kicked one of two penalty attempts - the second hitting the post late on.
Ten points adrift, Connacht stepped it up a gear on the restart and Matt Healy went close to scoring before fellow winger Poolman broke up a listless spell with his try, gathering replacement Muldowney's pass out of the tackle to score by the posts.
The Ospreys always seemed to have an extra gear when required and their Italian scrum-half Tebaldi sold a couple of dummies to grab a soft try from Connacht's perspective. Biggar converted for a 29-19 scoreline.
Connacht responded with Griffin's effort, which owed much to Poolman's bright build-up play, but the Ospreys stamped their authority during the concluding 18 minutes.
The composed visitors left no doubt over who would win the match with a spell of strong running and crisp passing that sent Hassler over for the clinching score in the 71st minute.
Biggar reached the 1,000-point mark by converting that try, and then added the extras to his skipper's easy finish, the final touchdown being created by replacement Richard Hibbard.