Out-half Dan Parks had kicked Connacht into the lead before lively Ospreys scrum-half Kahn Fotuali’i took a quick tap penalty to dive over for a 10th-minute try, converted by out-half Matthew Morgan.
The home side regained the initiative and Danie Poolman made a valuable break. The returning John Muldoon was held up on the line but Michael Swift set up quick ruck ball for openside Willie Faloon to dive over. Parks added the extras. Although Parks missed a subsequent penalty from just inside halfway, he made no mistake soon after as the pack once again had the Ospreys backpedaling.
Crucially, Parks also grabbed the first score after the restart as Morgel Ellen was penalised.
Although the Ospreys edged themselves into bonus territory the boot of Parks saw Connacht home.
Scorers for Connacht: Try: Faloon. Con: Parks. Pens: Parks 5.
Scorers for Ospreys: Try: Fotuali’i. Con: Morgan. Pen: Morgan.
CONNACHT: Henshaw, O’Halloran, EGriffin, Tonetti, Poolman, Parks, Marmion, Wilkinson, Harris-Wright, White, Swift, Kearney, Muldoon, Faloon, McKeon.
Replacements: Duffy for O’Halloran (15), O’Donohoe for Marmion (70), Ah You for Wilkinson (62), Loughney for White (41), Browne for Kearney (54), O’Connor for McKeon (66).
OSPREYS: Fussell, Haberfield, Isaacs, Spratt, John, Morgan, Fotuali’i, D Jones, Baldwin, Griffiths, A Jones, King, Bearman, Lewis, Allen, R Jones.
Replacements: R Jones for John (10), M Thomas for D Jones (75), Arhip for Griffiths (59), J Thomas for A Jones (66), Peers for Lewis (51), Webb for R Jones (66).
Referee: Giuseppe Vivarini (Italy).
Rabo Pro12: Edinburgh 16 Cardiff 17; Newport Gwent Dragons 3 Glasgow Warriors 60