Playing into the elements in the first half, an opportunist try from Kahn Fotuali’i converted by Matthew Morgan saw the Ospreys trail 13-7 at the break.
But they were unable to make an impact in the second half as the boot of Dan Parks guided Connacht to victory.
On a wet and windy night in Galway, the Ospreys were on the back foot from the first whistle as former Blues fly half Parks pinned the Welsh region back.
And when Cai Griffiths was penalised at a scrum, Parks slotted over a straightforward kick to put the hosts ahead.
Morgan then turned down an opportunity to go for the posts from a seemingly kickable position but was rewarded when Fotuali’I gave his side the lead.
The Samoan scrum half, who is bound for Northampton Saints at the end of the season, took a quick tap penalty and dived over though it was left to TMO Jude Quinn to confirm the try. Morgan’s conversion put the Ospreys ahead.
Connacht wasted no time in striking back, scoring their first try of the evening just a few minutes later through Willie Faloon, the flanker powering over from close range.
Parks added the conversion and a further penalty for a 13-7 interval advantage.
With the wind at their backs and facing just a six-point deficit at the restart, Ospreys hopes of a victory would have been high. But they found themselves further behind in the 47th minute when Parks kicked his third penalty.
Despite dominating territory, the visitors were struggling to get back into the game as they turned over possession on a number of occasions.Â
And Parks took full advantage to boot his team further upfield.
Trailing by nine points, the Ospreys narrowed the gap with a Morgan penalty but Parks replied with a kick of his own and a late drop goal to seal the win.
To rub salt in the wounds, James King received a yellow card in the dying moments to complete a disappointing night for the Ospreys.