Dan Biggar opened the scoring with penalty before Doug Howlett crossed for the first try.
Thomas O'Leary spotted a huge gap behind Ospreys wing Richard Fussell and his perfectly weighted chip bounced right into the arms of former All Black Howlett how touched down after 8 minutes.
Ronan O'Gara was off the mark with the conversion and also failed with two further penalties as the first half continued.
Biggar responded for the visitors almost immediately, kicking his second penalty from in front of the posts to re-take the lead.
On the stroke of half-time the Ospreys were penalised at the ruck and O'Gara finally found his kicking boots and calmly stroke the ball between the posts to take his side into the break ahead.
The Ospreys struck immediately after the re-start, Tommy Bowe picked off a wide pass and sprinting 70 yards to score under the posts and silence the home support. Biggar added the two points with the simplest of conversions.
Ospreys prop Paul James was shown the yellow card for collapsing the scrum on his own line and David Wallace took full advantage, barging his way over after repeated attacks, O'Gara added the conversion.
The Irish fly-half was lining up his next conversion just four minutes later as Johne Murphy touched down after a poor kick from Biggar.
Biggar responded with three points before O'Connell's red card. The British & Irish lock swung his arm which connected with Jonathan Thomas and was given his marching orders.
O'Connell's dismissal spurred the hosts on and they deserved this Round 3 victory.