The Wales scrum half, who missed the summer tour to South Africa through injury, struck first just before the break when his blindside snipe and chip ahead around a ruck 30 metres out from the Dragons line paved the way for the opening try of the game.
Walker was onto the bouncing ball as quick as a flash and once it was in his arms he simply veered towards the left corner to cross for a try out of nothing which Dan Biggar converted off the touchline.
That made it 10-3 to the visitors – Jason Tovey and Biggar had earlier swapped penalties – and proved to be a tipping point for the visitors. Having earlier had to cope with an aggressive Dragons scrum, they had been forced to soak up pressure, but were far more assured in the second half.
It took just eight minute for them to notch their second try after the re-start, although the Dragons had by then narrowed the gap with a penalty from their Wales Under 20 outside half Angus O’Brien, who was a replacement for Tovey.
Quick ball at a series of rucks in the home 22 allowed Webb to fire out some snappy passes before catching lock Rynier Bernardo unawares with a brilliant show and go 10 metres out to break clean through to score at the posts.
Biggar converted and the Ospreys were in firm control for the next 20 minutes before they lost Walker to the sin-bin for an aerial challenge on Tyler Morgan. O’Brien added further punishment with a wide angled penalty and then the teenager kept his calm to hammer over a 47 metre penalty to cut the gap to two points.
That set up a thrilling finale that included a 35 metre drop goal attempt that drifted a couple of feet wide. It was a feisty affair throughout, but for the second weekend running the Dragons ended up with a losing bonus point while the Ospreys ended with a victory.