The Dragons opened their Group A campaign with just one win from their first four games but after beating Scotland 2-1 in Cardiff last October, they then repeated the trick on Friday night at Hampden. The victory moves Chris Coleman's team up to third place, where they are seven points behind joint leaders Belgium and Croatia.
The Croatians now visit Swansea on Tuesday and Williams insists that, while the stakes are mounted high against a Welsh win, securing a ticket to next summer's finals in Brazil is still achievable. And he told Press Association Sport: "It keeps it alive for us. We have never said we could do anything after the start we had but we have always got that hope."
He added: "We just need to keep picking up points. There are plenty still to play for.
"We are on a decent run of form, which bodes well. We did well in the friendly the other day, so we have got two wins on the trot now.
"Scotland are a good team, and to go there on a night like Friday was massive. It showed the character of the team that we were able to come back from a goal down. But we just need to keep it going. We have got Croatia on Tuesday and that will be another tough one."
Wales secured the win with an Aaron Ramsey penalty and winner from Hal Robson-Kanu after fighting back from Grant Hanley's opener for the Scots in first-half stoppage time.
Ramsey was sent off in stoppage time for his late tackle on James McArthur but Wales had done enough to secure victory.
The fact their second-half recovery was achieved without the assistance of 25-goal Tottenham forward Gareth Bale - who limped off at the break due to ankle problems and a virus - was another satisfying factor for Swansea defender Williams.
He said: "It was a very important win for us. We need the points and there was a little bit extra riding on the game because it was against one of the Home Nations. It was massive. But we showed we can cope without Gareth."
Source: PA
Source: PA