Webster helped the national team keep a clean sheet in Gordon Strachan's opening match in charge against Estonia on Wednesday night.
And the centre-half captained his country for the first time at Pittodrie after Celtic midfielder Scott Brown was substituted on the hour mark.
It was a hugely encouraging display by the defender personally – and the Scotland rearguard as a whole – against albeit limited opposition at home.
The defence was never wholly convincing during Craig Levein's time in charge and the showing augurs well for the World Cup qualifiers against Wales and Serbia next month.
Webster, though, feels he will have to maintain his standards to retain his place for that double-header with former Rangers starlet Wilson now playing regularly.
Wilson, currently on loan at Hearts from Barclays Premier League giants Liverpool, won five Scotland caps under former manager Levein.
However, the 21-year-old has drifted out of the international picture since then as he has struggled to get a game at club level.
His new team-mate, though, predicts that could all be about to change.
"I think Danny Wilson has got real good quality," said Webster. "He just needs to play football which he is doing now.
"Danny is still a young man and has his whole career in front of him. He has played at international level before so I am sure it is an ambition of his.
"Getting the opportunity to play at Hearts now, he is definitely going to put himself in the shop window for progressing at international level."
He added: "It was nice to get the Scotland captaincy this week. Not a lot of people get that opportunity.
"I think we have got off to a good start under the new manager.
"The quality in the squad is exceptionally high. There are boys playing in the English Premier League coming off the bench.
"To have that strength in depth as a team will help us. If you look at up front then Steven Fletcher started, with Shaun Maloney in behind.
"Jamie Mackie, who plays in the Premier League week in week out, couldn't get on. From that point of view it must be good for the manager to be able to call upon these guys."