Director of rugby Ian McGeechan declared Wasps had put themselves "back in the competition" with consecutive Heineken Cup victories over Edinburgh.
Fly-half Dave Walder scored all the points as Wasps followed up their victory at Murrayfield last weekend with a gritty 19-11 win at Adams Park.
With Castres beating Leinster yesterday, Wasps’ victory sets up a pivotal showdown with the Irish group leaders at Twickenham when the Heineken Cup returns to action on January 17.
“We are back in the competition and that is the most important thing for us at this stage,” said McGeechan.
“Edinburgh was not an easy place to go and they are not an easy side to play. We knew they would try and make a statement against us today and I thought we handled it pretty well.”
Walder started at fly-half after Danny Cipriani spent the week fighting a stomach bug and produced a third consecutive man-of-the-match performance.
McGeechan added: “Defensively he was very good, his kicking was 100% - Danny did that last week - and he attacked the line and scored a try as well.
“He is playing good heads-up rugby with a lot of confidence.”
Wasps were more ambitious in the first half than at any point last week but they are still struggling for fluency and at times the second period degenerated into a lifeless kick-fest.
But after a disastrous start to the season, head coach Shaun Edwards believes Wasps are beginning to turn their fortunes around.
“Obviously we are delighted with a win. We are getting on the right side of these narrow margins now,” said Edwards.
“That Leinster game is almost England versus Ireland. It will be a pretty tasty match.
“As a unit we were pretty embarrassed with the way we performed over in Dublin (in a 41-11 defeat) and we will be pretty determined that day.”
Edinburgh head coach Andy Robinson rued two “missed opportunities” against a Wasps side that have been misfiring this season.
“They managed the game pretty well to win both games but you can see by the scoreline how close they have been,” he said.
“Last week was a missed opportunity and I thought at 8-7 if we came out and played with a bit of tempo and held onto the ball in attack we might have asked some questions of them.
“There was a lack of skill at times. We could execute our first-phase plays and we needed to do that to put Wasps under pressure.
“We scored one good try with a great line from Ben Cairns, which I was really pleased with, but we never threatened after that and our accuracy wasn’t good enough.”