After the break James Hook's penalty cut Leicester's lead to six points.
The Ospreys scored a classy try of their own through Nikki Walker, plus one from prop Duncan Jones, but were let down by James Hook's place-kicking.
First Biggar's swift pass found James Hook drifting just outside his marker and the centre raced through a gap to send Shane Williams racing over for a try on his 100th Ospreys appearance.
But the Ospreys claimed a losing bonus point after James Hook converted Nikki Walker's last-minute try.
Wales, by contrast, totalled 14 points from the boots of fly-half Stephen Jones and centre James Hook, the latter's late drop-goal giving Wales breathing space as Italy pressed in the final quarter.
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Two James Hook penalties and Gavin Henson's converted first-half try suggested an easy night for the Welsh.
An interception try by the outstanding James Hook, picking off Smit's pass, and Stephen Jones' conversion gave Wales a 16-3 lead.
Ospreys had matched Edinburgh's tally of four tries, but James Hook and Dan Biggar both missed crucial kicks.
Nikki Walker's converted try and a long-distance James Hook penalty was enough to see the visitors through.
Fly-half James Hook directed play in the driving wind and rain at Galway's Sportsground, landing a penalty before his delightful chip made Walker's try.
But tries from Adam Jones and James Hook brought the visitors back to within three points before Haskell's breakaway effort five minutes from time clinched victory.
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At fly-half Ireland's Ronan O'Gara and Wales' Stephen Jones are rubber-stamped but James Hook, Toby Flood, Danny Cipriani and maybe Cardiff Blues number 10 Nicky Robinson, after his performance against Gloucester on Saturday, are all in the frame.
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