The Magpies ended a run of three successive Barclays Premier League defeats with a 1-0 win over the midlands side at St James' Park on Saturday to reach the 40-point mark 10 games earlier than they managed it during the last campaign.
A hard-fought victory, which was secured by Loic Remy's injury-time strike, restored a measure of calm on Tyneside after another turbulent episode in the club's chequered recent history which saw manager Alan Pardew's future thrown into question once again.
However, he remains in post and, while European qualification now seems an unlikely target, Williamson and his team-mates are not prepared to concede that their season is effectively over.
The 30-year-old central defender said: "The last thing the lads want is for the season to peter out.
"We want to keep pushing and to prove we can look up the league rather than down the league.
"I thought the character shone through more than anything. I don't think there was a great deal of quality on the pitch, but that's what happens when a team lacks confidence.
"But what you have got to do is roll your sleeves up and do the basics and work as hard as you can and I thought that was what the team did.
"We did create chances, and I had a belief that as long, as we could keep the back door shut, we could always come up with something like that. Loic did and the lads are buzzing."
If Remy claimed the headlines with his late winner, Pardew cited an earlier vital interception by Williamson as the spark for a grandstand finish in which the France international also hit a post with the goal at his mercy.
He managed to cut out Christian Benteke's attempted through-ball which would otherwise have put the Magpies in deep trouble and, as the home crowd responded, so too did the players.
Pardew said: "They are on their break, it's probably their biggest chance of the second half, Willo falls on the ball when he is intercepting it.
"It was all a bit ugly, but suddenly the crowd went mad and it lifted us. You could see it mentally lift us.
"I am not sure it won us the game, but it was part of that little spell we had at the end. We were probably better at the end than we were for the rest of the game."
The win ended a demoralising run of five successive defeats at St James', four of them in the league, and went some of the way towards restoring a measure of confidence in a team which had wobbled alarmingly in the face of a selection crisis.
Yohan Cabaye's January departure for Paris St Germain would have had an impact even if he had been replaced, but the loss of Fabricio Coloccini and Cheick Tiote through injury and Remy through suspension at the same time compounded Pardew's problems.
A contrite Remy eventually marked his return in the best way possible and he has already set his sights on righting a further wrong when Newcastle head for Hull next weekend determined to avenge a 3-2 home defeat in September in which he scored both his side's goals.
He said: "I remember the game against Hull. It was a good game for me in terms of goals, but I remember we lost this game so, for me, it is going to be revenge to win this game."
Villa, who enjoyed periods of dominance, particularly in the first half, ultimately headed home empty-handed to contemplate a home clash with Norwich next Sunday, with both sides now just four points clear of the drop zone.
However, manager Paul Lambert is confident his players have learned from last season's flirtation with relegation.
He said: "You certainly hope it helps you, that's for sure. When you go through something, you know how to handle it the second time it maybe happens.
"But we are definitely a better outfit this time than we were last year. It's another good game for us. We are at home and it's a game that we will go and try to win."