The Ospreys maintained their recent good form with a 29-22 win over Ulster in the Magners League on Saturday.
The victory extended the Ospreys' unbeaten run at home to 14 games and marked some revenge for their 43-7 reversal at Ravenhill last autumn.
As well as two-try Walker, Shaun Connor contributed 19 points to the win.
Ulster gained a losing bonus point thanks to 17 points from the left boot of Paul Steinmetz.
It took the Ospreys until only the third minute to take the lead through the first of Connor's dropped-goals.
But the advantage was short-lived as Steinmetz slotted two penalties in the space of two minutes.
Gavin Henson was on hand to show his defensive abilities with an all-embracing tackle on Tommy Bowe which prevented an almost certain Ulster try.
A promising Ospreys attack, which saw Connor break through midfield, ended with the home outside-half putting over his second penalty - from a high tackle on Jonathan Thomas - to give his side a 9-6 advantage on 24 minutes.
And with their next attack the Ospreys extended that lead to 20 points with a well-worked try for Walker.
Just before the interval Steinmetz converted his third penalty - the longest of the trio - following a high tackle by Andrew Millward, to make it 16-9 at half-time.
Steinmetz made it four out of four with a penalty five minutes in to the second half as Ulster upped the tempo.
But from a concerted Ulster attack the Ospreys turned the ball over through Connor and hooker Huw Bennett sent Walker away on a 55-metre run for his second try.
Steinmetz kept Ulster in the game with a fifth successful penalty but Connor cancelled that out to restore an 11-point advantage.
That lead was then cut when Stephen Ferris scored Ulster's try from the restart converted by Steinmetz to set up a nervous finish for the home side.
But Connor had the last say with a second drop-goal.
Tries: Walker 2
Cons: Connor 2
Pens: Connor 3
Drops Goals: Connor 2
Pens: Steinmetz 5
Ospreys: 15 Gavin Henson, 14 Nikki Walker, 13 Tal Selley, 12 Andrew Bishop, 11 Richard Mustoe, 10 Shaun Connor, 9 Justin Marshall, 8 Jonathan Thomas, 7 Richard Pugh, 6 Andy Lloyd, 5 Mike Powell, 4 Brent Cockbain, 3 Andrew Millward, 2 Huw Bennett, 1 Paul James (c).
Replacements: 16 Barry Williams, 17 Cai Griffiths, 18 Chris Martenko, 19 Lee Beach, 20 Steve Tandy, 21 Jason Spice, 22 Stefan Terblanche.
Ulster: 15 Mark Bartholomeusz, 14 Tommy Bowe, 13 Paul Steinmetz, 12 Kevin Maggs, 11 Paul McKenzie, 10 Adam Larkin, 9 Kieran Campbell, 8 Roger Wilson, 7 Kieron Dawson, 6 Stephen Ferris, 5 Tim Barker, 4 Justin Harrison (c), 3 Bryan Young, 2 Paul Shields, 1 Justin Fitzpatrick,
Replacements: 16 Stuart Philpott, 17 Declan Fitzpatrick, 18 Ryan Caldwell, 19 David Pollock, 20 Paul Marshall, 21 Scott Young, 22 Bryn Cunningham.
Referee: Peter Allen (Scotland)
Touch judges: Tim Hayes (Wales), Gary Davies (Wales)