Both sides went into the game at Murrayfield on the back of dispiriting defeats on the opening weekend of the championship.
Scotland suffered a heavy defeat against England at Twickenham, showing little of the dogged determination which had served them so well in last year's campaign, while Wales were defeated by Ireland at the Millennium Stadium.
Hadden and Gareth Jenkins' charges therefore knew the match in wintry Edinburgh would shape the rest of theirÂ Six Nations season.
Despite both sides suggesting in the build-up that they intended to play an open game it turned out - perhaps in part due to the conditions - to be a turgid, try-less affair.
All the points came from the boots of opposing captains Chris Paterson and Stephen Jones, with the Scotland skipper making no mistake with his seven penalties as Hadden's side ground out a 21-9 victory.
Scotland now prepare to face Italy at home a week on Saturday with a boost to their confidence and the prospect of another successfulÂ Six Nations campaign on the back the giant strides made in 2006.
In contrast, Wales face the daunting prospect of travelling to face France in Paris and another championship slipping through their fingers following the halcyon days of 2005 under Mike Ruddock.
Dewey admits the pressure had been building up in the Scotland camp in the days before the match against Wales, with the knowledge it was such a pivotal game in their season.
He said: "After losing against England we knew we had to put in a big performance against England. It was win or bust really.
"I think you could see that right from the start with guys putting in big hits for the team, which was great to see.
"We felt the pressure before the match because we didn't want to lose three games in a row. It's been a while since that happened and we didn't want it to happen on Saturday.
"The guys came out and gave their all after the defeats to Australia and England and now we can look forward to the Italy game."