Ospreys went top of the Magners League despite an unconvincing performance against Connacht at the Liberty Stadium.
Dan Biggar, released for the match by the Wales squad, provided 14 points with a try and three penalties as the Ospreys just squeezed home.
Biggar found himself in the thick of the early action. First he missed a drop goal before being successful with a penalty.
Connacht drew level on 14 minutes with an Ian Keatley penalty.
Ospreys scored a spectacular try as full-back Gareth Owen ran in with real pace going through two men and then rounded the full-back as the home side led 8-3 after 19 minutes.
Connacht's endeavours were rewarded with a second penalty for Ian Keatley to reduce the Ospreys lead to 8-6 on 35 minutes.
In first-half injury time a flowing Ospreys attack ended with the award of a penalty which Biggar converted from the 22 to give his side an 11-6 interval lead.
Mike Phillips made his return from injury at half-time and almost immediately the Ospreys opened up a 13-point lead with a penalty and try for Biggar within the first nine minutes of the restart.
Biggar went in at the left corner after receiving a reverse pass from Owen.
But any hopes of then going for the bonus point win had to be delayed after second row Ian Evans was yellow-carded for a high tackle, and with the extra man Connacht grabbed a try through hooker Sean Cronin.
And 19-11 became 19-14 as Keatley converted a penalty from in front of the posts.
In injury time, despite being down a man due to Gavin Duffy's sin-binning, Connacht then cut the deficit to just two points with Keatley's fourth penalty.