The Saints had failed to score in their last four league matches but smashed five past Hamilton in an eight-goal thriller to the delight of their manager.
"I thought attacking-wise we were really good today. We moved the ball well, got in behind and took our chances which was pleasing to see," said Davidson.
"We conceded three goals so we can do better defensively but the character to keep going and going was pleasing.
"We couldn't score a goal at the start of the season and now we have 12 in two games so hopefully we can keep going.
"It's always difficult going into the lead because you have to keep going. All credit to Hamilton because they kept fighting and made it a game. It's probably a better game to watch than it is to manage."
The visitors raced into a three-goal lead in the opening half hour. Stevie May netted against his former club in just under a minute before David Wotherspoon doubled their advantage with a low strike.
May grabbed his second from a corner before Hamilton mounted a comeback, scoring twice before half-time through Ronan Hughes and Marios Ogkmpoe.
Accies pressed for an equaliser after the break but were susceptible on the break and Conway punished them after a devastating counter attack in the 69th minute.
The impressive Hughes grabbed his second with 10 minutes remaining to give the hosts hope, but Conway fired a stunning free-kick to send Accies bottom of the league.
Hamilton showed great resilience to battle their way back into the game and manager Brian Rice refused to be too downhearted.
"We scored three goals at home and it is not often you see Hamilton do that but we still did not take anything from the game," he said. "I am not disappointed with the effort, just the result.
"I get satisfaction from the effort they put in and there is a way of losing games and they gave it everything they had.
"You sink or swim and I did not see anybody jumping off the ship there but we gave ourselves too much to do."