Captain Greig Laidlaw believes Edinburgh are flourishing on the European stage because head coach Michael Bradley's methods have grown on the players.
Edinburgh set up a Heineken Cup semi-final against Ulster with a surprise 19-14 success over four-times champions Toulouse on Saturday.
Laidlaw, who kicked 14 points on Saturday, told BBC Scotland: "Michael's been hugely important. He has been a breath of fresh air for the club this year. He has brought in a sense of real direction on how he wants us to play the game."
He added: "The players maybe never bought right into it at the start of the season.
"But now we are really buying into what he's about and that's why we're getting these kind of results."
Edinburgh have twice suffered defeat against Ulster in the league this year, conceding 80 points in the process, but Laidlaw is convinced they can upset the odds again when they meet at the Aviva Stadium in Dublin on April 28.
"It is going to be a hard game," said the Scotland fly-half. "Ulster have been playing a lot of good rugby this year.
"They have a massive forward pack. They have some great players in there and some good South African players.
"It will be a tough test for us over in Ireland as well, but it was a tough test on Saturday and we did well against a big Toulouse pack - and I thought our forwards were brilliant on Saturday."