Though it was never a classic it gave Byrne, Shane Williams, Jonathan Thomas and Brent Cockbain useful run-outs in front of watching Wales coach Gareth Jenkins ahead of next Saturday's RBS 6 Nations visit to Paris to face France.
The opening 40 minutes never really got going although Connacht were always the more inventive with Paul Warwick varying play throughout.
But it was the Ospreys who broke a 29-minute deadlock with a penalty goal for outside-half Shaun Connor after the Irish province were adjudged offside. The home side's lead was shortlived however, with Warwick levelling after the Ospreys also went offside in their own half.
In the final two minutes of the half both defences were guilty of lapses.
First the Ospreys allowed Warwick to get a pass away in the tackle giving full-back David Slemen room to go over for a converted try by the posts.
But on the stroke of the interval the Ospreys got their first meaningful passing movement together with wing Nikki Walker having two significant parts to play in it before Byrne went over in the right corner.
It ended a pretty solid first 40 minutes for Byrne, who is being tipped to play full-back for Wales in Paris next Saturday with Kevin Morgan out injured.
And with an injury to Connor, Byrne took over the kicking duties in the second half. Though he missed his first two attempts at goal he was successful with his next three. Two penalties were followed by his conversion of skipper Paul James' try which followed the sin-binning of Connacht's replacement flanker Matt Lacey.
The Ospreys points kept on coming after that.
First Shane Williams put over a 30-metre drop-goal attempt and there was then a penalty try as the home pack put the squeeze on at a five-metre scrum.
Ospreys: 15. Lee Byrne 14. Nikki Walker 13. Tal Selley 12. Andrew Bishop 11. Shane Williams 10. Shaun Connor 9. Justin Marshall 1. Paul James 2. Huw Bennett 3. Andrew Millward 4. Brent Cockbain 5. Mike Powell 6. Lee Beach 7. Richie Pugh 8. Jonathan Thomas
|Connacht : 15. David Slemen 14. Darren Yapp 13. John Hearty 12. Mark McHugh 11. Danny Riordan 10. Paul Warwick 9. Conor O'Loughlin 1. Ray Hogan 2. John Fogarty 3. Stephen Knoop 4. David Gannon 5. Ryan Strudwick 6. John Muldoon 7. Ray Ofisa 8. Colm Rigney
Replacements: 16. Adrian Flavin 17. Brett Sturgess 18. Michael Swift 19. Matt Lacey 20. Chris Keane 21. Gavin Williams 22. Peter Durcan