Walker and Beck touched down in either half as the Ospreys over-came their poor record at Rodney Parade to beat Newport Gwent Dragons.
Dan Biggar converted both in a mixed kicking display though it was enough for the Ospreys to claim only their second win in Newport in 10 years.
It was another near-miss for the Dragons, five days after losing out 12-10 to Cardiff Blues, who could only manage a Tom Prydie penalty and remain in 11th place.
The Ospreys had previously only won once at Rodney Parade in nine years’ – and not since 2007 – but they got off to a flying start on their tenth visit. Walker finished in the left-hand corner as early as the third minute though the Dragons will be disappointed at the ease of the score.
Biggar, Andrew Bishop and Richard Fussell all combined to send the young wing scampering over for his fifth try of the campaign.
Biggar converted for a 7-0 lead that last 10 minutes until former Osprey Prydie struck with his second effort as the Dragons recovered from the early blow.
However despite their efforts and possession, the hosts found themselves facing a white wall as the Ospreys defence proved impregnable.
Biggar twice failed to extend the Ospreys 7-3 lead before half-time to leave the Dragons in contention.
Kahn Fotuali’i almost caught the Dragons off-guard with a clever box kick but opposite number Jonathan Evans scampered back to deny the Samoan.
Moments later at Fotuali’I again went close after he blocked Lewis Robling’s clearance.
Prydie was then called into last-ditch defensive action to snuff out the danger caused by Biggar’s delicate chip but the warning signs were clear.
Beck finally grabbed the Ospreys’ second when Robling was again charged down yards from his own try line.
This time it was the lunging body of Biggar that blocked the young fly-half’s kick to hand Beck an easy finish on 62 minutes.
