"I'm very happy," said Edwards, who watched his side overturn a 16-15 deficit to win 25-6 at Murrayfield.
"It was a really tense affair. It was a war of attrition. Both teams were desperate for a victory and, fortunately for us, we were on the right end of the scoreline."
Cpiriani kicked six penalties and a conversion for an individual tally of 20 points as Wasps kept their hopes of qualifying for the knockout stages very much alive.
"There were a couple of big plays from Mark van Gisbergen and Danny's goal kicking was exemplary," added Edwards.
"I think it was seven from seven and some of the kicks he made were from 45 or 50 metres.
"Danny's very happy and very comfortable playing for Wasps in the No10 shirt. He guided us around the pitch in attack and, like I said, his goal kicking was exemplary."
Wasps now face the same opposition at Adams Park next Sunday, with Edwards expecting an equally stern challenge.
"We're very, very cautious of the Edinburgh team. They won at Castres in their last away game so next week is another massive game for us.
"They're a very, very well-coached team. They've got some potent attacking threats and you can see why the Scotland team did well in the autumn internationals.
"Edinburgh are a team to be reckoned with and respected. We'll have a couple of days off and then we'll start preparing for a big game."