Matthaus hails Bulgaria performance
Ivelin Popov scored the winner three minutes after the break with a shot that went in off the post to give Bulgaria their first win in 2010.
Bulgaria suffered back-to-back defeats to England and Montenegro in their two opening Group G qualifiers but the win against Wales has revived their chances of reaching the Euro 2012 finals.
Matthaus, who was appointed coach last month, said he was not pleased with the first half.
"Players seem to have forgotten that they're playing against Wales - a team searching for victory at any cost and until the very end," said Germany's former World Cup-winning captain.
"But it was a different story after the interval and we showed that we're the better team. Our second-half performance was an indication of how we're able to play and I think it was a deserved win."
Matthaus, 49, replaced Stanimir Stoilov, who resigned after the 1-0 home loss to Montenegro. He became Bulgaria's first foreign coach since 1966.
Montenegro top the standings with nine points from three matches, followed by England with six points from two matches. Bulgaria are third with three points.
Bulgaria will next meet Switzerland in March, though winger Martin Petrov faces a suspension after receiving his second yellow card of the campaign.