Mark McHugh was the hero at the Sportsground as he booted four second-half penalties to send the Ospreys packing and Connacht to the top of the Magners Celtic League table after a 15-10 victory.
McHugh, with two of his kicks from inside his own half, booted five penalties in all as the Ospreys floundered after leading 10-3 at the interval.
It was McHugh's loose grubber kick that former All Black Justin Marshall collected on the way to scoring the game's only try, just before half-time.
But Connacht's superb fighting spirit, typified by their grizzled pack, saw them deservedly come from behind for their first win in four meetings with the Welsh region.
The Ospreys, starting with 15 internationals, were marginally the better side during a dull first half.
Into the wind, McHugh chipped over his first penalty from 32 metres to hand Connacht a ninth-minute lead. Marshall drove his troops on and young fly-half James Hook took the second of two penalty opportunities to draw level by the 29th minute.
The Connacht pack, which had Ospreys tighthead Adam Jones under a good deal of pressure in the scrum, carved open a late chance.
However, McHugh took the wrong option from second phase ball and his kick was gobbled up by Marshall and the 33-year-old scrum half showed a great turn of pace to race virtually the length of the field and score in the right corner.
Hook added the conversion for a seven-point Ospreys lead.
Yet with revenge for last season's 44-16 defeat at the same venue clearly on their minds, Connacht roared out for the second half and McHugh kicked a penalty within seven minutes to reduce the arrears.
The former Ireland international right-footed over his third success of the night, six minutes later, from all of 55 metres to turn the heat right up on the former champions.
The Ospreys then dug their heels in with Adam Jones only just bundled into touch five metres from the hosts' line.
Drama followed when McHugh ensured a sweet victory as he banged over another penalty from his own half, and after Marshall had been fortunate to remain on the field for a punch on Tom Tierney, the Connacht number 10 bisected the posts again, eight minute into injury-time.
